Structural equation modeling (SEM) is a diverse set of methods used by scientists doing both observational and experimental research. SEM is used mostly in the social and behavioral sciences but it is also used in epidemiology, business, and other fields. A definition of SEM is difficult without reference to technical language, but a good starting place is the name itself.

SEM involves a model representing how various aspects of some phenomenon are thought to causally connect to one another. Structural equation models often contain postulated causal connections among some latent variables (variables thought to exist but which can't be directly observed). Additional causal connections link those latent variables to observed variables whose values appear in a data set. The causal connections are represented using equations but the postulated structuring can also be presented using diagrams containing arrows as in Figures 1 and 2. The causal structures imply that specific patterns should appear among the values of the observed variables. This makes it possible to use the connections between the observed variables' values to estimate the magnitudes of the postulated effects, and to test whether or not the observed data are consistent with the requirements of the hypothesized causal structures.

The boundary between what is and is not a structural equation model is not always clear but SE models often contain postulated causal connections among a set of latent variables (variables thought to exist but which can't be directly observed, like an attitude, intelligence or mental illness) and causal connections linking the postulated latent variables to variables that can be observed and whose values are available in some data set. Variations among the styles of latent causal connections, variations among the observed variables measuring the latent variables, and variations in the statistical estimation strategies result in the SEM toolkit including confirmatory factor analysis, confirmatory composite analysis, path analysis, multi-group modeling, longitudinal modeling, partial least squares path modeling, latent growth modeling and hierarchical or multilevel modeling.

SEM researchers use computer programs to estimate the strength and sign of the coefficients corresponding to the modeled structural connections, for example the numbers connected to the arrows in Figure 1. Because a postulated model such as Figure 1 may not correspond to the worldly forces controlling the observed data measurements, the programs also provide model tests and diagnostic clues suggesting which indicators, or which model components, might introduce inconsistency between the model and observed data. Criticisms of SEM methods hint at: disregard of available model tests, problems in the model's specification, a tendency to accept models without considering external validity, and potential philosophical biases.

A great advantage of SEM is that all of these measurements and tests occur simultaneously in one statistical estimation procedure, where all the model coefficient are calculated using all information from the observed variables. This means the estimates are more accurate than if a researcher were to calculate each part of the model separately.

History

Structural equation modeling (SEM) began differentiating itself from correlation and regression when Sewall Wright provided explicit causal interpretations for a set of regression-style equations based on a solid understanding of the physical and physiological mechanisms producing direct and indirect effects among his observed variables. The equations were estimated like ordinary regression equations but the substantive context for the measured variables permitted clear causal, not merely predictive, understandings.  O. D. Duncan introduced SEM to the social sciences in his 1975 book and SEM blossomed in the late 1970's and 1980's when increasing computing power permitted practical model estimation. In 1987 Hayduk provided the first book-length introduction to structural equation modeling with latent variables, and this was soon followed by Bollen's popular text (1989).

Different yet mathematically related modeling approaches developed in psychology, sociology, and economics. Early Cowles Commission work on simultaneous equations estimation centered on Koopman and Hood's (1953) algorithms from transport economics and optimal routing, with maximum likelihood estimation, and closed form algebraic calculations, as iterative solution search techniques were limited in the days before computers. The convergence of two of these developmental streams (factor analysis from psychology, and path analysis from sociology via Duncan) produced the current core of SEM. One of several programs Karl Jöreskog developed at Educational Testing Services, LISREL embedded latent variables (which psychologists knew as the latent factors from factor analysis) within path-analysis-style equations (which sociologists inherited from Wright and Duncan). The factor-structured portion of the model incorporated measurement errors which permitted measurement-error-adjustment, though not necessarily error-free estimation, of effects connecting different postulated latent variables.

Traces of the historical convergence of the factor analytic and path analytic traditions persist as the distinction between the measurement and structural portions of models; and as continuing disagreements over model testing, and whether measurement should precede or accompany structural estimates. Viewing factor analysis as a data-reduction technique deemphasizes testing, which contrasts with path analytic appreciation for testing postulated causal connections – where the test result might signal model misspecification. The friction between factor analytic and path analytic traditions continue to surface in the literature and on SEMNET – a free listserve circulating SEM postings to more than 3,000 registrants, supported by a University of Alabama listserv. The SEMNET archive can be searched for user-specified topics, and many of the 2023 updates to this Wikipedia page were previously circulated on SEMNET for knowledgeable review and comment.

Wright's path analysis influenced Hermann Wold, Wold's student Karl Jöreskog, and Jöreskog's student Claes Fornell, but SEM never gained a large following among U.S. econometricians, possibly due to fundamental differences in modeling objectives and typical data structures. The prolonged separation of SEM's economic branch led to procedural and terminological differences, though deep mathematical and statistical connections remain. The economic version of SEM can be seen in SEMNET discussions of endogeneity, and in the heat produced as Judea Pearl's approach to causality via directed acyclic graphs (DAG's) rubs against economic approaches to modeling. Discussions comparing and contrasting various SEM approaches are available but disciplinary differences in data structures and the concerns motivating economic models make reunion unlikely. Pearl extended SEM from linear to nonparametric models, and proposed causal and counterfactual interpretations of the equations. Nonparametric SEMs permit estimating total, direct and indirect effects without making any commitment to linearity of effects or assumptions about the distributions of the error terms.

SEM analyses are popular in the social sciences because computer programs make it possible to estimate complicated causal structures, but the complexity of the models introduces substantial variability in the quality of the results. Some, but not all, results are obtained without the "inconvenience" of understanding experimental design, statistical control, the consequences of sample size, and other features contributing to good research design.

General steps and considerations
The following considerations apply to the construction and assessment of many structural equation models.

Model specification

Building or specifying a model requires attending to:
 the set of variables to be employed,
 what is known about the variables,
 what is presumed or hypothesized about the variables' causal connections and disconnections,
 what the researcher seeks to learn from the modeling,
 and the cases for which values of the variables will be available (kids? workers? companies? countries? cells? accidents? cults?).

Structural equation models attempt to mirror the worldly forces operative for causally homogeneous cases – namely cases enmeshed in the same worldly causal structures but whose values on the causes differ and who therefore possess different values on the outcome variables. Causal homogeneity can be facilitated by case selection, or by segregating cases in a multi-group model. A model's specification is not complete until the researcher specifies:
 which effects and/or correlations/covariances are to be included and estimated,
 which effects and other coefficients are forbidden or presumed unnecessary,
 and which coefficients will be given fixed/unchanging values (e.g. to provide measurement scales for latent variables as in Figure 2).

The latent level of a model is composed of endogenous and exogenous variables. The endogenous latent variables are the true-score variables postulated as receiving effects from at least one other modeled variable. Each endogenous variable is modeled as the dependent variable in a regression-style equation. The exogenous latent variables are background variables postulated as causing one or more of the endogenous variables and are modeled like the predictor variables in regression-style equations. Causal connections among the exogenous variables are not explicitly modeled but are usually acknowledged by modeling the exogenous variables as freely correlating with one another. The model may include intervening variables – variables receiving effects from some variables but also sending effects to other variables. As in regression, each endogenous variable is assigned a residual or error variable encapsulating the effects of unavailable and usually unknown causes. Each latent variable, whether exogenous or endogenous, is thought of as containing the cases' true-scores on that variable, and these true-scores causally contribute valid/genuine variations into one or more of the observed/reported indicator variables.

The LISREL program assigned Greek names to the elements in a set of matrices to keep track of the various model components. These names became relatively standard notation, though the notation has been extended and altered to accommodate a variety of statistical considerations.  Texts and programs "simplifying" model specification via diagrams or by using equations permitting user-selected variable names, re-convert the user's model into some standard matrix-algebra form in the background. The "simplifications" are achieved by implicitly introducing default program "assumptions" about model features with which users supposedly need not concern themselves. Unfortunately, these default assumptions easily obscure model components that leave unrecognized issues lurking within the model's structure, and underlying matrices.

Two main components of models are distinguished in SEM: the structural model showing potential causal dependencies between endogenous and exogenous latent variables, and the measurement model showing the causal connections between the latent variables and the indicators. Exploratory and confirmatory factor analysis models, for example, focus on the causal measurement connections, while path models more closely correspond to SEMs latent structural connections.

Modelers specify each coefficient in a model as being free to be estimated, or fixed at some value. The free coefficients may be postulated effects the researcher wishes to test, background correlations among the exogenous variables, or the variances of the residual or error variables providing additional variations in the endogenous latent variables. The fixed coefficients may be values like the 1.0 values in Figure 2 that provide a scales for the latent variables, or values of 0.0 which assert causal disconnections such as the assertion of no-direct-effects (no arrows) pointing from Academic Achievement to any of the four scales in Figure 1. SEM programs provide estimates and tests of the free coefficients, while the fixed coefficients contribute importantly to testing the overall model structure. Various kinds of constraints between coefficients can also be used. The model specification depends on what is known from the literature, the researcher's experience with the modeled indicator variables, and the features being investigated by using the speific model structure.

There is a limit to how many coefficients can be estimated in a model. If there are fewer data points than the number of estimated coefficients, the resulting model is said to be "unidentified" and no coefficient estimates can be obtained. Reciprocal effect, and other causal loops, may also interfere with estimation.

Estimation of free model coefficients

Model coefficients fixed at zero, 1.0, or other values, do not require estimation because they already have specified values. Estimated values for free model coefficients are obtained by maximizing fit to, or minimizing difference from, the data relative to what the data's features would be if the free model coefficients took on the estimated values. The model's implications for what the data should look like for a specific set of coefficient values depends on:
a) the coefficients' locations in the model (e.g. which variables are connected/disconnected),
b) the nature of the connections between the variables (covariances or effects; with effects often assumed to be linear),
c) the nature of the error or residual variables (often assumed to be independent of, or causally-disconnected from, many variables),
and d) the measurement scales appropriate for the variables (interval level measurement is often assumed).

A stronger effect connecting two latent variables implies the indicators of those latents should be more strongly correlated. Hence, a reasonable estimate of a latent's effect will be whatever value best matches the correlations between the indicators of the corresponding latent variables – namely the estimate-value maximizing the match with the data, or minimizing the differences from the data. With maximum likelihood estimation, the numerical values of all the free model coefficients are individually adjusted (progressively increased or decreased from initial start values) until they maximize the likelihood of observing the sample data – whether the data are the variables' covariances/correlations, or the cases' actual values on the indicator variables. Ordinary least squares estimates are the coefficient values that minimize the squared differences between the data and what the data would look like if the model was correctly specified, namely if all the model's estimated features correspond to real worldly features.

The appropriate statistical feature to maximize or minimize to obtain estimates depends on the variables' levels of measurement (estimation is generally easier with interval level measurements than with nominal or ordinal measures), and where a specific variable appears in the model (e.g. endogenous dichotomous variables create more estimation difficulties than exogenous dichotomous variables). Most SEM programs provide several options for what is to be maximized or minimized to obtain estimates the model's coefficients. The choices often include maximum likelihood estimation (MLE), full information maximum likelihood (FIML), ordinary least squares (OLS), weighted least squares (WLS), diagonally weighted least squares (DWLS), and two stage least squares.

One common problem is that a coefficient's estimated value may be underidentified because it is insufficiently constrained by the model and data. No unique best-estimate exists unless the model and data together sufficiently constrain or restrict a coefficient's value. For example, the magnitude of a single data correlation between two variables is insufficient to provide estimates of a reciprocal pair of modeled effects between those variables. The correlation might be accounted for by one of the reciprocal effects being stronger than the other effect, or the other effect being stronger than the one, or by effects of equal magnitude. Underidentified effect estimates can be rendered identified by introducing additional model and/or data constraints. For example, reciprocal effects can be rendered identified by constraining one effect estimate to be double, triple, or equivalent to, the other effect estimate, but the resultant estimates will only be trustworthy if the additional model constraint corresponds to the world's structure. Data on a third variable that directly causes only one of a pair of reciprocally causally connected variables can also assist identification. Constraining a third variable to not directly cause one of the reciprocally-causal variables breaks the symmetry otherwise plaguing the reciprocal effect estimates because that third variable must be more strongly correlated with the variable it causes directly than with the variable at the "other" end of the reciprocal which it impacts only indirectly.  Notice that this again presumes the properness of the model's causal specification – namely that there really is a direct effect leading from the third variable to the variable at this end of the reciprocal effects and no direct effect on the variable at the "other end" of the reciprocally connected pair of variables. Theoretical demands for null/zero effects provide helpful constraints assisting estimation, though theories often fail to clearly report which effects are allegedly nonexistent.

Model assessment

Model assessment depends on the theory, the data, the model, and the estimation strategy. Hence model assessments consider:
 whether the data contain reasonable measurements of appropriate variables,
 whether the modeled case are causally homogeneous, (It makes no sense to estimate one model if the data cases reflect two or more different causal networks.)
 whether the model appropriately represents the theory or features of interest, (Models are unpersuasive if they omit features required by a theory, or contain coefficients inconsistent with that theory.)
 whether the estimates are statistically justifiable, (Substantive assessments may be devastated: by violating assumptions, by using an inappropriate estimator, and/or by encountering non-convergence of iterative estimators.)
 the substantive reasonableness of the estimates, (Negative variances, and correlations exceeding 1.0 or -1.0, are impossible. Statistically possible estimates that are inconsistent with theory may also challenge theory, and our understanding.)
 the remaining consistency, or inconsistency, between the model and data. (The estimation process minimizes the differences between the model and data but important and informative differences may remain.)

Research claiming to test or "investigate" a theory requires attending to beyond-chance model-data inconsistency. Estimation adjusts the model's free coefficients to provide the best possible fit to the data. The output from SEM programs includes a matrix reporting the relationships among the observed variables that would be observed if the estimated model effects actually controlled the observed variables' values. The "fit" of a model reports match or mismatch between the model-implied relationships (often covariances) and the corresponding observed relationships among the variables. Large and significant differences between the data and the model's implications signal problems. The probability accompanying a  (chi-squared) test is the probability that the data could arise by random sampling variations if the estimated model constituted the real underlying population forces. A small  probability reports it would be unlikely for the current data to have arisen if the modeled structure constituted the real population causal forces – with the remaining differences attributed to random sampling variations.

If a model remains inconsistent with the data despite selecting optimal coefficient estimates, an honest research response reports and attends to this evidence (often a significant model  test).  Beyond-chance model-data inconsistency challenges both the coefficient estimates and the model's capacity for adjudicating the model's structure, irrespective of whether the inconsistency originates in problematic data, inappropriate statistical estimation, or incorrect model specification.
Coefficient estimates in data-inconsistent ("failing") models are interpretable, as reports of how the world would appear to someone believing a model that conflicts with the available data. The estimates in data-inconsistent models do not necessarily become "obviously wrong" by becoming statistically strange, or wrongly signed according to theory. The estimates may even closely match a theory's requirements but the remaining data inconsistency renders the match between the estimates and theory unable to provide succor. Failing models remain interpretable, but only as interpretations that conflict with available evidence.

Replication is unlikely to detect misspecified models which inappropriately-fit the data. If the replicate data is within random variations of the original data, the same incorrect coefficient placements that provided inappropriate-fit to the original data will likely also inappropriately-fit the replicate data. Replication helps detect issues such as data mistakes (made by different research groups), but is especially weak at detecting misspecifications after exploratory model modification – as when confirmatory factor analysis (CFA) is applied to a random second-half of data following exploratory factor analysis (EFA) of first-half data.

A modification index is an estimate of how much a model's fit to the data would "improve" (but not necessarily how much the model's structure would improve) if a specific currently-fixed model coefficient were freed for estimation. Researchers confronting data-inconsistent models can easily free coefficients the modification indices report as likely to produce substantial improvements in fit. This simultaneously introduces a substantial risk of moving from a causally-wrong-and-failing model to a causally-wrong-but-fitting model because improved data-fit does not provide assurance that the freed coefficients are substantively reasonable or world matching. The original model may contain causal misspecifications such as incorrectly directed effects, or incorrect assumptions about unavailable variables, and such problems cannot be corrected by adding coefficients to the current model. Consequently, such models remain misspecified despite the closer fit provided by additional coefficients. Fitting yet worldly-inconsistent models are especially likely to arise if a researcher committed to a particular model (for example a factor model having a desired number of factors) gets an initially-failing model to fit by inserting measurement error covariances "suggested" by modification indices. MacCallum (1986) demonstrated that "even under favorable conditions, models arising from specification serchers must be viewed with caution." Model misspecification may sometimes be corrected by insertion of coefficients suggested by the modification indices, but many more corrective possibilities are raised by employing a few indicators of similar-yet-importantly-different latent variables.

"Accepting" failing models as "close enough" is also not a reasonable alternative. A cautionary instance was provided by Browne, MacCallum, Kim, Anderson, and Glaser who addressed the mathematics behind why the  test can have (though it does not always have) considerable power to detect model misspecification.  The probability accompanying a  test is the probability that the data could arise by random sampling variations if the current model, with its optimal estimates, constituted the real underlying population forces. A small  probability reports it would be unlikely for the current data to have arisen if the current model structure constituted the real population causal forces – with the remaining differences attributed to random sampling variations.  Browne, McCallum, Kim, Andersen, and Glaser presented a factor model they viewed as acceptable despite the model being significantly inconsistent with their data according to . The fallaciousness of their claim that close-fit should be treated as good enough was demonstrated by Hayduk, Pazkerka-Robinson, Cummings, Levers and Beres  who demonstrated a fitting model for Browne, et al.'s own data by incorporating an experimental feature Browne, et al. overlooked. The fault was not in the math of the indices or in the over-sensitivity of  testing. The fault was in Browne, MacCallum, and the other authors forgetting, neglecting, or overlooking, that the amount of ill fit cannot be trusted to correspond to the nature, location, or seriousness of problems in a model's specification.

Many researchers tried to justify switching to fit-indices, rather than testing their models, by claiming that  increases (and hence   probability decreases) with increasing sample size (N). There are two mistakes in discounting  on this basis. First, for proper models,  does not increase with increasing N, so if  increases with N that itself is a sign that something is detectably problematic. And second, for models that are detectably misspecified,  increase with N provides the good-news of increasing statistical power to detect model misspecification (namely power to detect Type II error). Some kinds of important misspecifications cannot be detected by , so any amount of ill fit beyond what might be reasonably produced by random variations warrants report and consideration. The  model test, possibly adjusted, is the strongest available structural equation model test.

Numerous fit indices quantify how closely a model fits the data but all fit indices suffer from the logical difficulty that the size or amount of ill fit is not trustably coordinated with the severity or nature of the issues producing the data inconsistency.  Models with different causal structures which fit the data identically well, have been called equivalent models. Such models are data-fit-equivalent though not causally equivalent, so at least one of the so-called equivalent models must be inconsistent with the world's structure. If there is a perfect 1.0 correlation between X and Y and we model this as X causes Y, there will be perfect fit and zero residual error. But the model may not match the world because Y may actually cause X, or both X and Y may be responding to a common cause Z, or the world may contain a mixture of these effects (e.g. like a common cause plus an effect of Y on X), or other causal structures. The perfect fit does not tell us the model's structure corresponds to the world's structure, and this in turn implies that getting closer to perfect fit does not necessarily correspond to getting closer to the world's structure – maybe it does, maybe it doesn't. This makes it incorrect for a researcher to claim that even perfect model fit implies the model is correctly causally specified. For even moderately complex models, precisely equivalently-fitting models are rare. Models almost-fitting the data, according to any index, unavoidably introduce additional potentially-important yet unknown model misspecifications. These models constitute a greater research impediment.

This logical weakness renders all fit indices "unhelpful" whenever a structural equation model is significantly inconsistent with the data, but several forces continue to propagate fit-index use. For example, Dag Sorbom reported that when someone asked Karl Joreskog, the developer of the first structural equation modeling program, "Why have you then added GFI?" to your LISREL program, Joreskog replied "Well, users threaten us saying they would stop using LISREL if it always produces such large chi-squares. So we had to invent something to make people happy. GFI serves that purpose." The  evidence of model-data inconsistency was too statistically solid to be dislodged or discarded, but people could at least be provided a way to distract from the "disturbing" evidence. Career-profits can still be accrued by developing additional indices, reporting investigations of index behavior, and publishing models intentionally burying evidence of model-data inconsistency under an MDI (a mound of distracting indices). There seems no general justification for why a researcher should "accept" a causally wrong model, rather than attempting to correct detected misspecifications. And some portions of the literature seems not to have noticed that "accepting a model" (on the basis of "satisfying" an index value) suffers from an intensified version of the criticism applied to "acceptance" of a null-hypothesis. Introductory statistics texts usually recommend replacing the term "accept" with "failed to reject the null hypothesis" to acknowledge the possibility of Type II error. A Type III error arises from "accepting" a model hypothesis when the current data are sufficient to reject the model.

Whether or not researchers are committed to seeking the world's structure is a fundamental concern. Displacing test evidence of model-data inconsistency by hiding it behind index claims of acceptable-fit, introduces the discipline-wide cost of diverting attention away from whatever the discipline might have done to attain a structurally-improved understanding of the discipline's substance. The discipline ends up paying a real costs for index-based displacement of evidence of model misspecification. The frictions created by disagreements over the necessity of correcting model misspecifications will likely increase with increasing use of non-factor-structured models, and with use of fewer, more-precise, indicators of similar yet importantly-different latent variables.

The considertions relevant to using fit indices include checking:
  whether data concerns have been addressed (to ensure data mistakes are not driving model-data inconsistency);

  whether criterion values for the index have been investigated for models structured like the researcher's model (e.g. index criterion based on factor structured models are only appropriate if the researcher's model actually is factor structured);

  whether the kinds of potential misspecifications in the current model correspond to the kinds of misspecifications on which the index criterion are based (e.g. criteria based on simulation of omitted factor loadings may not be appropriate for misspecification resulting from failure to include appropriate control variables);

  whether the researcher knowingly agrees to disregard evidence pointing to the kinds of misspecifications on which the index criteria were based. (If the index criterion is based on simulating a missing factor loading or two, using that criterion acknowledges the researcher's willingness to accept a model missing a factor loading or two.);

  whether the latest, not outdated, index criteria are being used (because the criteria for some indices tightened over time);

  whether satisfying criterion values on pairs of indices are required (e.g. Hu and Bentler report that some common indices function inappropriately unless they are assessed together.);
  whether a model test is, or is not, available. (A  value, degrees of freedom, and probability will be available for models reporting indices based on .)

 and whether the researcher has considered both alpha (Type I) and beta (Type II) errors in making their index-based decisions (E.g. if the model is significantly data-inconsistent, the "tolerable" amount of inconsistency is likely to differ in the context of medical, business, social and psychological contexts.).

Some of the more commonly used fit statistics include
 Chi-square
 A fundamental test of fit used in the calculation of many other fit measures. It is a function of the discrepancy between the observed covariance matrix and the model-implied covariance matrix. Chi-square increases with sample size only if the model is detectably misspecified.
 Akaike information criterion (AIC)
 An index of relative model fit: The preferred model is the one with the lowest AIC value.

 where k is the number of parameters in the statistical model, and L is the maximized value of the likelihood of the model.
 Root Mean Square Error of Approximation (RMSEA)
Fit index where a value of zero indicates the best fit. Guidelines for determining a "close fit" using RMSEA are highly contested.
 Standardized Root Mean Squared Residual (SRMR)
 The SRMR is a popular absolute fit indicator. Hu and Bentler (1999) suggested .08 or smaller as a guideline for good fit.
 Comparative Fit Index (CFI)
In examining baseline comparisons, the CFI depends in large part on the average size of the correlations in the data.  If the average correlation between variables is not high, then the CFI will not be very high. A CFI value of .95 or higher is desirable.

The following table provides references documenting these, and other, features for some common indices: the RMSEA (Root Mean Square Error of Approximation), SRMR (Standardized Root Mean Squared Residual), CFI (Confirmatory Fit Index), and the TLI (the Tucker-Lewis Index). Additional indices such as the AIC (Akaike Information Criterion) can be found in most SEM introductions. For each measure of fit, a decision as to what represents a good-enough fit between the model and the data reflects the researcher's modeling objective (perhaps challenging someone else's model, or improving measurement); whether or not the model is to be claimed as having been "tested"; and whether the researcher is comfortable "disregarding" evidence of the index-documented degree of ill fit.

Sample size, power, and estimation

Researchers agree samples should be large enough to provide stable coefficient estimates and reasonable testing power but there is no general consensus regarding specific required sample sizes, or even how to determine appropriate sample sizes. Recommendations have been based on the number of coefficients to be estimated, the number of modeled variables, and Monte Carlo simulations addressing specific model coefficients.  Sample size recommendations based on the ratio of the number of indicators to latents are factor oriented and do not apply to models employing single indicators having fixed nonzero measurement error variances.  Overall, for moderate sized models without statistically difficult-to-estimate coefficients, the required sample sizes (N's) seem roughly comparable to the N's required for a regression employing all the indicators.

The larger the sample size, the greater the likelihood of including cases that are not causally homogeneous. Consequently, increasing N to improve the likelihood of being able to report a desired coefficient as statistically significant, simultaneously increases the risk of model misspecification, and the power to detect the misspecification. Researchers seeking to learn from their modeling (including potentially learning their model requires adjustment or replacement) will strive for as large a sample size as permitted by funding and by their assessment of likely population-based causal heterogeneity/homogeneity. If the available N is huge, modeling sub-sets of cases can control for variables that might otherwise disrupt causal homogeneity. Researchers fearing they might have to report their model's deficiencies are torn between wanting a larger N to provide sufficient power to detect structural coefficients of interest, while avoiding the power capable of signaling model-data inconsistency. The huge variation in model structures and data characteristics suggests adequate sample sizes might be usefully located by considering other researchers' experiences (both good and bad) with models of comparable size and complexity that have been estimated with similar data.

Interpretation

Causal interpretations of SE models are the clearest and most understandable but those interpretations will be fallacious/wrong if the model's structure does not correspond to the world's causal structure. Consequently, interpretation should address the overall status and structure of the model, not merely the model's estimated coefficients. Whether a model fits the data, and/or how a model came to fit the data, are paramount for interpretation. Data fit obtained by exploring, or by following successive modification indices, does not guarantee the model is wrong but raises serious doubts because these approaches are prone to incorrectly modeling data features. For example, exploring to see how many factors are required preempts finding the data are not factor structured, especially if the factor model has been "persuaded" to fit via inclusion of measurement error covariances. Data's ability to speak against a postulated model is progressively eroded with each unwarranted inclusion of a "modification index suggested" effect or error covariance. It becomes exceedingly difficult to recover a proper model if the initial/base model contains several misspecifications.

Direct-effect estimates are interpreted in parallel to the interpretation of coefficients in regression equations but with causal commitment. Each unit increase in a causal variable's value is viewed as producing a change of the estimated magnitude in the dependent variable's value given control or adjustment for all the other operative/modeled causal mechanisms. Indirect effects are interpreted similarly, with the magnitude of a specific indirect effect equaling the product of the series of direct effects comprising that indirect effect. The units involved are the real scales of observed variables' values, and the assigned scale values for latent variables. A specified/fixed 1.0 effect of a latent on a specific indicator coordinates that indicator's scale with the latent variable's scale. The presumption that the remainder of the model remains constant or unchanging may require discounting indirect effects that might, in the real world, be simultaneously prompted by a real unit increase. And the unit increase itself might be inconsistent with what is possible in the real world because there may be no known way to change the causal variable's value. If a model adjusts for measurement errors, the adjustment permits interpreting latent-level effects as referring to variations in true scores.

SEM interpretations depart most radically from regression interpretations when a network of causal coefficients connects the latent variables because regressions do not contain estimates of indirect effects. SEM interpretations should convey the consequences of the patterns of indirect effects that carry effects from background variables through intervening variables to the downstream dependent variables. SEM interpretations encourage understanding how multiple worldly causal pathways can work in coordination, or independently, or even counteract one another. Direct effects may be counteracted (or reinforced) by indirect effects, or have their correlational implications counteracted (or reinforced) by the effects of common causes. The meaning and interpretation of specific estimates should be contextualized in the full model.

SE model interpretation should connect specific model causal segments to their variance and covariance implications. A single direct effect reports that the variance in the independent variable produces a specific amount of variation in the dependent variable's values, but the causal details of precisely what makes this happens remains unspecified because a single effect coefficient does not contain sub-components available for integration into a structured story of how that effect arises. A more fine-grained SE model incorporating variables intervening between the cause and effect would be required to provide features constituting a story about how any one effect functions. Until such a model arrives each estimated direct effect retains a tinge of the unknown, thereby invoking the essence of a theory. A parallel essential unknownness would accompany each estimated coefficient in even the more fine-grained model, so the sense of fundamental mystery is never fully eradicated from SE models.

Even if each modeled effect is unknown beyond the identity of the variables involved and the estimated magnitude of the effect, the structures linking multiple modeled effects provide opportunities to express how things function to coordinate the observed variables – thereby providing useful interpretation possibilities. For example, a common cause contributes to the covariance or correlation between two effected variables, because if the value of the cause goes up, the values of both effects should also go up (assuming positive effects) even if we do not know the full story underlying each cause. (A correlation is the covariance between two variables that have both been standardized to have variance 1.0). Another interpretive contribution might be made by expressing how two causal variables can both explain variance in a dependent variable, as well as how covariance between two such causes can increase or decrease explained variance in the dependent variable. That is, interpretation may involve explaining how a pattern of effects and covariances can contribute to decreasing a dependent variable's variance. Understanding causal implications implicitly connects to understanding "controlling", and potentially explaining why some variables, but not others, should be controlled.  As models become more complex these fundamental components can combine in non-intuitive ways, such as explaining how there can be no correlation (zero covariance) between two variables despite the variables being connected by a direct non-zero causal effect.

The statistical insignificance of an effect estimate indicates the estimate could rather easily arise as a random sampling variation around a null/zero effect, so interpreting the estimate as a real effect becomes equivocal. As in regression, the proportion of each dependent variable's variance explained by variations in the modeled causes are provided by R2, though the Blocked-Error R2 should be used if the dependent variable is involved in reciprocal or looped effects, or if it has an error variable correlated with any predictor's error variable.

The caution appearing in the Model Assessment section warrants repeat. Interpretation should be possible whether a model is or is not consistent with the data. The estimates report how the world would appear to someone believing the model – even if that belief is unfounded because the model happens to be wrong. Interpretation should acknowledge that the model coefficients may or may not correspond to "parameters" – because the model's coefficients may not have corresponding worldly structural features.

Adding new latent variables entering or exiting the original model at a few clear causal locations/variables contributes to detecting model misspecifications which could otherwise ruin coefficient interpretations. The correlations between the new latent's indicators and all the original indicators contribute to testing the original model's structure because the few new and focused effect coefficients must work in coordination with the model's original direct and indirect effects to coordinate the new indicators with the original indicators. If the original model's structure was problematic, the sparse new causal connections will be insufficient to coordinate the new indicators with the original indicators, thereby signaling the inappropriateness of the original model's coefficients through model-data inconsistency. The correlational constraints grounded in null/zero effect coefficients, and coefficients assigned fixed nonzero values, contribute to both model testing and coefficient estimation, and hence deserve acknowledgment as the scaffolding supporting the estimates and their interpretation.

Interpretations become progressively more complex for models containing interactions, nonlinearities, multiple groups, multiple levels, and categorical variables. For interpretations of coefficients in models containing interactions, see { reference needed }, for multilevel models see { reference needed }, for longitudinal models see, { reference needed }, and for models containing categoric variables see { reference needed }.  Effects touching causal loops, reciprocal effects, or correlated residuals also require slightly revised interpretations.

Careful interpretation of both failing and fitting models can provide research advancement. To be dependable, the model should investigate academically informative causal structures, fit applicable data with understandable estimates, and not include vacuous coefficients. Dependable fitting models are rarer than failing models or models inappropriately bludgeoned into fitting, but appropriately-fitting models are possible.

The multiple ways of conceptualizing PLS models complicate interpretation of PLS models. Many of the above comments are applicable if a PLS modeler adopts a realist perspective by striving to ensure their modeled indicators combine in a way that matches some existing but unavailable latent variable. Non-causal PLS models, such as those focusing primarily on R2 or out-of-sample predictive power, change the interpretation criteria by diminishing concern for whether or not the model's coefficients have worldly counterparts. Money can be made from statistically significant predictors even if the modeler is not interested in the worldly structural forces providing the predictive power. The fundamental features differentiating the five PLS modeling perspectives discussed by Rigdon, Sarstedt and Ringle point to differences in PLS modelers' objectives, and corresponding differences in model features warranting interpretation.

Caution should be taken when making claims of causality even when experiments or time-ordered investigations have been undertaken. The term causal model must be understood to mean "a model that conveys causal assumptions", not necessarily a model that produces validated causal conclusions—maybe it does maybe it does not.  Collecting data at multiple time points and using an experimental or quasi-experimental design can help rule out certain rival hypotheses but even a randomized experiments cannot fully rule out threats to causal claims. No research design can fully guarantee causal structures.

Controversies and Movements
Structural equation modeling is fraught with controversies, many of which surfaced in discussions on SEMNET and which remain available in SEMNET's archive. SEMNET is a free listserv made available by the University of Alabama. Researchers from the factor analytic tradition commonly attempt to reduce sets of multiple indicators to fewer, more manageable, scales or factor-scores for later use in path-structured models. This constitutes a stepwise process with the initial measurement step providing scales or factor-scores which are to be used later in a path-structured model. This stepwise approach seems obvious but actually confronts severe underlying deficiencies. The segmentation into steps interferes with thorough checking of whether the scales or factor-scores validly represent the indicators, and/or validly report on latent level effects.  A structural equation model simultaneously incorporating both the measurement and latent-level structures not only checks whether the latent factors appropriately coordinates the indicators, it also checks whether that same latent simultaneously appropriately coordinates each latent's indictors with the indicators of theorized causes and/or consequences of that latent. If a latent is unable to do both these styles of coordination, the validity of that latent is questioned, and a scale or factor-scores purporting to measure that latent is questioned. The SEMNET disagreements swirled around respect for, or disrespect of, evidence challenging the validity of postulated latent factors. The simmering, sometimes boiling, SEMNET discussions resulted in a special issue of the journal Structural Equation Modeling focused on a target article by Hayduk and Glaser  followed by several comments and a rejoinder, all made freely available, thanks to the efforts of George Marcoulides.

These discussions fueled disagreement over whether or not structural equation models should be tested for consistency with the data, and model testing became the next focus of SEMNET discussions. The SEMNETers having  path-modeling histories tended to defend careful model testing while those with factor-histories tended to defend fit-indexing rather than fit-testing. This round of SEMNET discussions led to a target article in Personality and Individual Differences by Paul Barrett  who said: "In fact, I would now recommend banning ALL such indices from ever appearing in any paper as indicative of model "acceptability" or "degree of misfit"." (page 821). Barrett's article was also accompanied by commentary from both perspectives.

The controversy over model testing declined as SEMNET moved toward requiring clear report of significant model-data inconsistency. Scientists do not get to ignore, or fail to report, evidence just because they do not like what the evidence reports. The requirement of attending to evidence pointing toward model misspecification underpins more recent SEMNET concern for addressing "endogeneity" – a style of model misspecification that interferes with estimation due to lack of independence of error/residual variables. In general, the controversy over the causal nature of structural equation models, including factor-models, has also been declining. Even Stan Mulaik, a factor-analysis stalwart, has acknowledged the causal basis of factor models. The comments by Bollen and Pearl regarding myths about causality in the context of SEM reinforced the centrality of causal thinking in the context of SEM.

A briefer SEMNET controversy focused on competing models. Comparing competing models can be very helpful but there are fundamental issues that cannot be resolved by creating two models and retaining the better fitting model. The statistical sophistication of presentations like Levy and Hancock (2007), for example, makes it easy to overlook that a researcher might begin with one terrible model and one atrocious model, and end by retaining the structurally terrible model because some index reports it as better fitting than the atrocious model. It is unfortunate that  even otherwise strong SEM texts like Kline (2016) remain disturbingly weak in their presentation of model testing.  Overall, the contributions that can be made by structural equation modeling depend on careful and detailed model assessment, even if a failing model happens to be the best available.

An additional controversy that touched the fringes of the previous controversies awaits ignition on SEMNET. Factor models and theory-embedded factor structures having multiple indicators tend to fail, and dropping weak indicators tends to reduce the model-data inconsistency. Reducing the number of indicators leads to concern for, and controversy over, the minimum number of indicators required to support a latent variable in a structural equation model. Researchers tied to factor tradition can be persuaded to reduce the number of indicators to three per latent variable, but three or even two indicators may still be inconsistent with a proposed underlying factor common cause. Hayduk and Littvay (2012) discussed how to think about, defend, and adjust for measurement error, when using only a single indicator for each modeled latent variable. Single indicators have been used effectively in SE models for a long time, but controversy remains only as far away as a reviewer who has considered measurement form only the factor analytic perspective.

Though declining, traces of these controversies are scattered throughout the SEM literature, and you can easily incite disagreement by asking: What should be done with models that are significantly inconsistent with the data? Or by asking: Does model simplicity override respect for evidence of data inconsistency? Or, what weight should be given to indexes which show close or not-so-close data fit for some models? Or, should we be especially lenient toward, and "reward", parsimonious models that are inconsistent with the data? Or, given that the RMSEA condones disregarding some real ill fit for each model degree of freedom, doesn't that mean that people testing models with null-hypotheses of non-zero RMSEA are doing deficient model testing? Considerable variation in statistical sophistication is required to cogently address such questions, though responses will likely center on the non-technical matter of whether or not researchers are required to report and respect evidence.

Extensions, modeling alternatives, and statistical kin

 Categorical dependent variables
 Categorical intervening variables
 Copulas {reference required}
 Fusion validity models
 item response theory models
 Latent class models
 Latent growth modeling
 Link functions
 Longitudinal models
 Measurement invariance models
 Mixture model,lLatent class models
 Multilevel models, hierarchical models (e.g. people nested in groups)
 Multiple group modelling with or without constraints between groups (genders, cultures, test forms, languages, etc.)
 Multi-method multi-trait models
 Random intercepts models
 Structural Equation Model Trees

Software
Structural equation modeling programs differ widely in their capabilities and user requirements.  Generally, the "simpler" or "more convenient" the user input, the greater the number of implicit model assumptions, and the greater the risk of problems created by insufficient attention to research design, methodology, measurement, estimation, or overlooked modeling problems. Good practice requires reporting both the program used, and the version of the program used.

 LISREL (not free) the first full SEM software, introduced basic notation https://ssicentral.com/index.php/products/lisrel/
 Mplus (not free)  https://www.statmodel.com/
 SEM in Stata (not free)   https://www.stata.com/features/structural-equation-modeling/
 sem (free R program)
 Lavaan (free R program)   https://cran.r-project.org/web/packages/lavaan/index.html
 OpenMX (free R program)  https://cran.r-project.org/web/packages/OpenMx/index.html
 AMOS (not free)  https://www.ibm.com/products/structural-equation-modeling-sem
 EQs  (not free)  https://www.azom.com/software-details.aspx?SoftwareID=11
 Stata
 SmartPLS

See also

Abbreviatons
CFA = Confirmatory Factor Analysis

CFI = Comparative Fit Index

DWLS = Diagonally Weighted Least Squares

EFA = Exploratory Factor Analysis

ESEM = Exploratory Structural Equation Modeling

GFI = Goodness of Fit Index

MIIV = Model Implied Instrumental Variables

OLS = Ordinary Least Squares

RMSEA = Root Mean Square Error of Approximation

RMSR = Root Mean Squared Residual

SRMR = Standardized Root Mean Squared Residual

SEM = Structural Equation Model or Modeling

WLS = Weighted Least Squares

 = Chi square

References

Bibliography

Further reading

 Bartholomew, D. J., and Knott, M. (1999) Latent Variable Models and Factor Analysis Kendall's Library of Statistics, vol. 7, Edward Arnold Publishers,
 Bentler, P.M. & Bonett, D.G. (1980), "Significance tests and goodness of fit in the analysis of covariance structures", Psychological Bulletin, 88, 588–606.
 Bollen, K. A. (1989). Structural Equations with Latent Variables. Wiley,
 Byrne, B. M. (2001) Structural Equation Modeling with AMOS - Basic Concepts, Applications, and Programming.LEA,
 Goldberger, A. S. (1972). Structural equation models in the social sciences. Econometrica 40, 979- 1001.

 Hoyle, R H (ed) (1995) Structural Equation Modeling: Concepts, Issues, and Applications. SAGE,

.

External links
 Structural equation modeling page under David Garson's StatNotes, NCSU
 Issues and Opinion on Structural Equation Modeling, SEM in IS Research
 The causal interpretation of structural equations (or SEM survival kit) by Judea Pearl 2000.
 Structural Equation Modeling Reference List by Jason Newsom: journal articles and book chapters on structural equation models
 Handbook of Management Scales, a collection of previously used multi-item scales to measure constructs for SEM

Graphical models
Latent variable models
Regression models
Structural equation models

Structural equation modeling


The N 15 was a trunk road (Route Nationale) in France.

Route
The RN 15 links the A13 to Le Havre via Rouen and Yvetot.

The RN 15 originates at junction 14 on the A13 autoroute in the Yvelines département near Bonnières-sur-Seine. The road's first few kilometres are notoriously dangerous as the road is a continuous decline towards the river Seine from the A13 autoroute to the RN 13.

After crossing the RN 13, the RN 15 follows the Seine towards Vernon. The RN 15 straightens and leaves the river, passing the town of Gaillon. The road runs parallel to the A13 autoroute and passes through the Forêt de Louviers heading North and over the river at Pont-de-l'Arche onto the right bank of the Seine.

The road follows the river bank overlooked by surrounding cliffs including the Roches de Saint-Adrien. The road meets the Route nationale 14 and enters the capital of Normandy, Rouen.

The N15 heads Northwest from the city centre and towards Yvetot. It enters the town of Yvetot to continue westwards. The road passes near the town of Bolbec, passes the A29 autoroute, Harfleur and enters Le Havre, ending at the city town hall.

History
The N 15 was numbered N 13BIS from the 1950s until the end of the 1970s reclassification scheme. The RN 13BIS replaced the RN 182 (between Bonnières-sur-Seine and Rouen) and the RN 14 (between Rouen and Le Havre).Until 1972, the RN 15 was going from Pontoise to Dieppe; this road has been changed in RD 915 except in the Eure where it is called RD 15BIS.In 2006, the RN 15 has also been changed in a départementale and is now numbered RD 6015 in the Eure and Seine-Maritime départements and D 915 in the Yvelines. Nowadays, the RN 15 is limited to the crossing of Rouen.

References

015
Transport in Normandy

Route nationale 15


David S. Lee (李信麟; pinyin: Lǐ Xìnlín) is the CEO, president and Chairman of the Board of eOn Communications Corporation, a telecom services company based in Kennesaw, Georgia.  Lee was born in China around 1938.

Education
Lee received a B.S. in mechanical engineering from Montana State University in 1960.  He obtained an M.S. in the same field from North Dakota State University.  He has received an honorary doctorate from Montana State University in 1993.

Career
Lee has served as the CEO of eOn Communications Corporation since 2003 and has performed as the Chairman of the board of that company since 1991.  From 1985 to 1988, Lee was President and Chairman of Data Technology Corporation, a computer peripheral company. Prior to 1985, he was Group Executive and Chairman of the Business Information Systems Group of ITT Corporation.  He was also President of ITT subsidiary ITT Qume, formerly Qume Corporation, a computer systems peripherals company which Lee co-founded in 1973 prior to its acquisition by ITT Corporation in 1978.

Lee serves on the corporate boards of ESS Technology, Inc., Linear Technology, iBassis and Daily Wellness Company.

Public service
Lee was appointed to the board of the Regents of the University of California in 1994 and served his full term which ended 2006.  He has also been a member of the Board of Governors for California Community Colleges.

He was an advisor to Presidents Bush and Clinton on the Advisory Committee on Trade Policy and Negotiation (Office of the U.S. Trade Representative/Executive Office of the President) and to former Governor Wilson through the California Economic Development Corporation and the council on California Competitiveness. He is a member of the President's Council on the 21st Century Workforce, appointed by President George W. Bush.

Further reading

External links
Forbes magazine profile
UC Board of Regents bio
eOn Communications bio

Montana State University alumni
American people of Chinese descent
American chief executives
University of California regents
Members of Committee of 100
1930s births
Living people

David S. Lee


David Holland (5 April 1948 – 16 January 2018) was an English drummer, born in Northampton, England. Holland is best remembered for his time with the bands Trapeze from 1969 to 1979 and Judas Priest from 1979 to 1989.

Early life

At the age of six Holland began piano lessons, but soon developed a "mania for the drums" in his own words and begged his parents to let him have a set. After his first appearance as a stand-in for a local band, Holland realized he wanted to be a musician. When he was 14 years old, he supplemented his pocket money by playing with another local band called The Drumbeats, and selling furniture and carpets.

As a youngster, Holland listened to traditional jazz. He cited his first rock influence as Johnny Kidd and the Pirates. Later, he became interested in funk music in the vein of Booker T & the MG's, the blues rock of Free and progressive–psychedelic music of Traffic.

Career

Early bands
In early 1965 he was with Northampton band Dorian Gray. Later that year Holland was persuaded to leave and join The Liberators who had recording and management contracts ready within a few weeks to evolve into Pinkerton's Assorted Colours, a pop band that put autoharp to good use, taking after The Loving Spoonful. In 1966 a single, "Mirror Mirror" (released 15 January 1966 on Decca, produced by future The Moody Blues producer Tony Clarke), peaked at No. 8 in the UK Singles Chart.

Finders Keepers
Holland stayed with the band until August 1968, when he joined Finders Keepers, a pop cover outfit. However, Holland continued studio session work. He did not play on a 1969 No. 5 hit single "Smile a Little Smile for Me" released by the band that used to be Pinkerton's Assorted Colours under the name of The Flying Machine.

Finders Keepers, who were soon joined by Mel Galley (guitar) and Glenn Hughes (bass), recorded several singles, with some of the songs now available on various compilations. Soon afterwards the threesome joined forces with vocalist and winds player John Jones and multi-instrumentalist Terry Rowley of The Montanas fame to form a quintet called Trapeze (the band name was Terry Rowley's idea).

Trapeze
Trapeze appeared in the British TV show Colour Me Pop and soon was swamped with offers of recording contracts, including one from The Beatles' Apple. Trapeze, however, settled for the newly formed Threshold label, belonging to The Moody Blues members. The band would soon open for The Moodies and other well-known acts. On Threshold, the band released three records, the debut as a quintet and the rest as a power trio.

Trapeze were gaining momentum at the time, especially in the southern United States, but lost a major contributor as Glenn Hughes decided to leave the band and join Deep Purple for the recording of their Burn album.

Mel Galley and Dave Holland added a bass player and a second guitarist. Dave Holland and Mel Galley also toured as part of John Lodge (musician) – Justin Hayward (of The Moody Blues fame) band The Blue Jays (Blue Jays (album)).

In 1978 Trapeze recorded their last studio LP, Running/Hold On.

Earlier on, both Galley and Holland lent a hand in the recording of Glenn Hughes' first solo album, Play Me Out, offering a unique blend of psychedelic jazz funk. Holland was assisted by Mark Nauseef on percussion.

In 1979 and 1980, Holland recorded some drum parts for Justin Hayward's solo albums, Songwriter and Night Flight.

Judas Priest
Holland left Trapeze and joined Judas Priest in August 1979. He played drums on many of Judas Priest's platinum albums, such as British Steel, Screaming for Vengeance, Defenders of the Faith, Turbo and Ram It Down.

During the 1980s, Holland also collaborated with guitarist Robin George, as part of his band Life and on George's solo project, Dangerous Music.

In 1989, personal problems (health and family issues) and musical differences forced Holland to leave Judas Priest. He was replaced by original Saints Or Sinners drummer Scott Travis, who had also previously played in the band Racer X.

Later career
Throughout the 1990s, besides touring with briefly reformed Trapeze and filling in for various bands like The Screaming Jets during their European tours, Holland gave drum clinics and private lessons, managed and produced bands such as UK band The Love Garden and the Swedish "teen funk trio" Shutlanger Sam (fronted by Kim Fransson who later had a solo career where he collaborated with among others hit songwriters Andreas Carlsson and Desmond Child) whom Holland introduced in person at a show with his former Trapeze bandmate Glenn Hughes in Vänersborg 1996, and played on various recordings of his former mates. In 1996, he participated in sessions that involved Glenn Hughes, Tony Iommi of Black Sabbath fame, and keyboardist Don Airey. In 1998, a collaboration with Al Atkins, Judas Priest's original singer, was released, featuring a few covers of early Priest songs that Holland did not originally play on. Judas Priest with Atkins at the helm had supported Trapeze in 1971.

Imprisonment
In 2004, Holland was arrested and later found guilty by a jury at Northampton Crown Court of one count of attempted rape and five counts of indecent assault against a 17-year-old male with learning difficulties. The offences occurred at Holland's rural English home in 2002 against a boy who had hired Holland to give him drum lessons. The jury also found a co-accused, 22-year-old Spiros Laouitaris, not guilty of four counts of indecent assault. Following the verdict, Judge Charles Wide told the court that Holland had "deliberately and calculatedly planned a strategy to abuse a boy who he knew was exceptionally vulnerable". Holland had steadfastly denied all charges, telling the court "There might have been the odd hug or something like that. I know it is politically incorrect nowadays, but kids like to be shown a bit of affection." It was revealed at trial that the victim had occasionally spent the night at Holland's house while taking lessons, and his parents learned of what Holland was doing when they received a letter from their son detailing the sexual abuse. He was sentenced to eight years in prison. In an interview during the criminal proceedings, Holland revealed publicly for the first time that he was bisexual.

Holland had recently completed some recording sessions with guitarist Tony Iommi. When word of his arrest became public, Iommi had Holland's drum tracks removed and re-recorded by Jimmy Copley, not wanting any association with a convicted sex offender.

Holland was scheduled for release from prison in 2012 and had reportedly served his full sentence that year.

In late 2006, Holland told author Neil Daniels in a letter from prison that he was in the process of writing his autobiography. Holland also stated his intent to appeal his conviction, saying "I was convicted of a crime that I didn't commit, and like so many others in similar situations to the one in which I find myself, an offense that never even existed in the first place...". He also railed against the legal system itself, telling Daniels "There is absolutely no difference whatsoever between the criteria that is permitted to be applied in sex offences now and that which was applied in cases of witchcraft in the 17th century."

Death
On 18 January 2018 it was announced that Holland had died a few days previously. No cause of death was provided.

On 22 January 2018, Spanish newspaper El Progreso reported that Holland had died on 16 January at Hospital Universitario Lucus Augusti in Lugo, Spain. Holland had been living in the nearby town of A Fonsagrada. The newspaper reported that Holland's remains had been cremated. However, a doctor had said that the death was due to lung cancer.

Discography

With Pinkerton's Assorted Colours
 Mirror Mirror / She don't care (single) (1965)
 Don't stop loving me baby / Will ya? (single) (1966)
 Magic Rocking Horse / It Ain't right (single) (1966) (as "Pinkerton's Colours")
 Mum and dad / On a street car (single) (1967) (as "Pinkerton's Colours")
 There's nobody I'd sooner love / Duke's Jetty (single) (1968) (as "Pinkerton's")
 Kentucky Woman / Behind the mirror (single) (1968) (as "Pinkerton's")

With Trapeze
 Trapeze (1970)
 Medusa (1970)
 You Are the Music...We're Just the Band (1972)
 The Final Swing (1974) (compilation, 2 previously unreleased songs)
 Hot Wire (1974)
 Trapeze (1975)
 Running (1978) aka Hold On (1979)
 Welcome to the Real World – Live at the Borderline 1992 (1998)
 Live Way Back to the Bone (1998) (previously unreleased compilation of live songs 1970–1972)
 Live at the Boat Club 1975 (2003)

With Blue Jays
 Live At Lancaster University, 1975 (The Moody Blues – Timeless Flight box set CD7, 2013)

With Glenn Hughes
 Play Me Out (1977)

With Justin Hayward
 Songwriter (1977)
 Night Flight (only the song "Crazy Lovers") (1980)

With Robin George
 Too late (released as "Life"; single; b-side: Castles) (1980)
 The History 12" (EP; recorded 1979–1981) (1983)
 Dangerous Music (only the song "Showdown", recorded 1979–1981) (1985)
 History (recorded 1979–1981) (2014)

With Judas Priest
 British Steel (1980)
 Point of Entry (1981)
 Screaming for Vengeance (1982)
 Defenders of the Faith (1984)
 Turbo (1986)
 Priest...Live! (1987)
 Ram It Down (1988)

With Marchesi
 Encrucijada (1992)

With Tony Iommi
 Eighth Star (1996) (unofficial release; later  released in 2004 as The 1996 DEP Sessions, with Holland's drum tracks re-recorded by Jimmy Copley)

With Al Atkins
 Victim of Changes (album) (1998)

Bibliography
 Personal recollections of Bob Ketchum
 Steve Gett, Metal Mania (1984)
 Judas Priest Tourbooks

References

1948 births
2018 deaths
Bisexual male musicians
British people convicted of attempted rape
English people convicted of indecent assault
English heavy metal drummers
English prisoners and detainees
English rock drummers
Finders Keepers (band) members
Judas Priest members
English LGBT musicians
English bisexual people
Musicians from Wolverhampton
Trapeze (band) members
Deaths from lung cancer in Spain
20th-century English LGBT people
21st-century English LGBT people

Dave Holland (drummer)


Xoom was an early dot-com company that provided free unlimited space web hosting, similar to GeoCities. The domain "xoom.com" is now held by the Xoom Corporation, an international-focused money transfer website run by PayPal.

History
Xoom was founded by Chris Kitze in September 1996 as a download website offering free clipart and a productivity suite including a word-processing application, centering on a word processor based on Wordstar.

In March 1997, Xoom became a web hosting (offering 100 MB) and an e-mail hosting website. The company acquired several small service providers in 1997 and 1998, including Paralogic, creator of ParaChat, which was the largest chat network on the web at the time, and PageCount, a web counter service. The main revenue sources for the company were direct marketing via email to members and banner advertising.

Funding
The company was funded by a former Lycos executive who had previously started Creative Multimedia (Portland, OR), Aris Multimedia (Marina del Rey, CA) and Point Communications (New York, NY), and angel investors who invested a total of $10M in common stock.  No venture capital was raised and the company went public in December 1998 (ticker symbol: XMCM).  Around that time, it was ranked as the 13th most popular site on the web by Media Metrix.  In May 1999, a deal was announced to use Xoom.com as a vehicle for NBC's internet ventures, that combined Snap.com (owned by CNET and NBC), and  various NBC internet assets plus $400M of NBC on-air promotion to form NBC Internet (NBCi).  At that time, the combined entity was ranked as the 7th most popular site on the web by Media Metrix.

Reception
Xoom was both criticized and praised for its strict policies on violations of terms of service. A short-lived experiment in franchising and licensing the Xoom software platform and business model in 1998 led to an Italian website, xoom.it, which is still in operation and owned by Virgilio.

References

Motley Fool article on Xoom.com
Wired article about NBCi

External links
Official Website (Archived)
Managed WordPress Hosting

Web 1.0
Web hosting
Dot-com bubble
Defunct online companies
Internet properties established in 1996
Internet properties disestablished in 2001

Xoom (web hosting)


Dr. Daniel Faraday is a fictional character on the ABC television series Lost played by Jeremy Davies. Faraday is introduced in the Season 4 premiere as a physicist from the Queen's College, University of Oxford. He suffers from short-term memory loss, possibly due to his experiments with radioactivity. He is part of the team aboard the  freighter Kahana that is offshore the island. Throughout his time on the series, Faraday plays an important role by sharing his knowledge of time travel. After time traveling to 1977, Faraday is shot and killed by Eloise Hawking (Alice Evans) who is unaware that he is her son.

Jeremy Davies was cast in the role because of the "tremendous intelligence that seems to emanate from him" and was one of the writer-producers' favorite character actors. Davies was critically praised for his performance and critics were generally disappointed by the character's death in season five. UGO.com named him one of the best TV nerds.

Arc

Background
Daniel was born to Eloise Hawking (Fionnula Flanagan)  and Charles Widmore (Alan Dale), both of whom were Others. Eloise raised Daniel on her own, hiding the identity of his father from him and pushing him to develop a scientific mind, much to the detriment of his social life and casual pursuits. After graduating from the University of Oxford with his girlfriend Theresa Spencer, Daniel was offered a £1.5 million grant by industrialist Charles Widmore. In the 1990s, Daniel started working as a physicist at The Queen's College, Oxford, with controversial experiments including sending a subject's consciousness through time. His initial tests on lab rats resulted in their deaths, which led to the abandonment of his studies. During his tenure, Daniel encountered Desmond Hume (Henry Ian Cusick), who was suffering from temporal displacement trapping him between 1996 and 2004. Daniel helped to ground Desmond's consciousness by telling him to find a constant in both time frames, which Desmond decided was to be Penny (Sonya Walger). This encounter had a profound effect on Daniel, reaffirming the legitimacy of his time-displacement theories and prompted him to resume his abandoned experiments. Daniel eventually performed similar experiments on Theresa, but she ended up suffering from temporal displacement as Desmond had and eventually fell into a coma, with temporary periods of lucidity.

The funds for her continuing care were provided by Charles Widmore. As a result of Theresa's fate, Oxford fired Daniel and quietly removed all references to him ever having been at the university. At some point, Daniel also performed an experiment upon himself, resulting in long-term memory damage. While in Essex, Massachusetts, Daniel saw a news report covering the discovery of the apparent wreckage of Oceanic Flight 815 in the depths of the Sunda Trench. Widmore approached Daniel and after informing him that the Sunda Trench wreckage was a hoax, urged him to go to the island, which he said would heal him of his plight. At first, Daniel was reluctant, but Eloise convinced him to go. Daniel is then recruited into a covert team alongside Charlotte Lewis (Rebecca Mader), Miles Straume (Ken Leung) and Frank Lapidus (Jeff Fahey), which is organized by Matthew Abaddon (Lance Reddick) and led by Naomi Dorrit (Marsha Thomason). Their mission was to travel to the island, find Ben Linus (Michael Emerson), the then current leader of the Others, and disable the Dharma Initiative station called the Tempest, which contained poisonous gases.

Season 4
Faraday first arrives on the island by parachuting out of a helicopter on December 23, 2004. After setting foot on the island, Faraday's memory problem slowly diminishes. He then encounters the survivors of Oceanic Flight 815, who are believed to be dead by the world at large. On the island, Faraday starts conducting an experiment regarding the island's unique passage of time. After reuniting with Charlotte, Faraday sneaks off with her to the Tempest Dharma Initiative station, where they neutralize a potential source of poison gas. Later, the corpse of the freighter's doctor washes ashore. Jack Shephard (Matthew Fox) confronts Faraday and he is forced to confess that the freighter upon which they arrived was not sent to the island to rescue the survivors. Around this time, Daniel realizes the Secondary Protocol, detailing the whereabouts of Ben Linus, has been activated by Widmore, necessitating their immediate departure from the island. Faraday begins to ferry survivors to the freighter, but Charlotte and Miles choose to remain on the island. Daniel and five survivors are caught midway between the Kahana and the island when the Kahana blows up and the island is "moved" by Ben Linus.

Season 5
When Ben causes the island to vanish, Charlotte, Faraday and the remaining survivors begin to travel through time. After the survivors are sent to the past, Faraday lures Desmond out of the Swan Dharma Initiative station, telling him to find Daniel's mother once Desmond is off the island.  Upon jumping further to the past, Faraday and the group are captured by the Others in 1954. The Others mistake them for military personnel and Faraday is forced to disable a hydrogen bomb labelled "Jughead". During this time period, he confesses his love for Charlotte. After telling the Others that they must bury the bomb, the survivors experience another time jump. The time jumps cause Charlotte to experience nosebleeds, headaches, and double vision, and she eventually collapses. As she dies, Charlotte tells Faraday she remembers living on the island as a child, and recognizes him as the man who told her not to return once she left the island. After John Locke (Terry O'Quinn) stops the time jumps, the remaining survivors are stranded in 1974. Faraday and his group move into the Barracks and under false pretenses, join the DHARMA Initiative. Despite the option to board the DHARMA submarine and "go back to the real world", the survivors from 2004 stay on the island together in the hope that they can somehow return to the time that they knew and Faraday becomes a scientist for DHARMA. Faraday then leaves the island and joins the DHARMA headquarters in Ann Arbor, Michigan.

In 1977, Daniel arrives back on the island and sets out to stop the construction of the Swan Station before drilling hits the electromagnetic "energy pocket", which ultimately results in the crash of Flight 815. Faraday plans to detonate the hydrogen bomb "Jughead" and destroy the unstable electromagnetic energy so no one would have to be pushing a button to save the world and Flight 815 would not crash. Before putting his plan into action, Daniel visits a young Charlotte, telling her never to return to the island once she leaves. Daniel then travels to the Others' camp with Jack and Kate Austen (Evangeline Lilly) to obtain the bomb. He breaks into their camp and threatens to shoot Richard Alpert (Nestor Carbonell). However, he is shot by his mother, Eloise Hawking. Before Daniel dies, he tells Eloise he is her son and she sent him to the island despite knowing he would die.

Afterlife
In the afterlife, in which Oceanic Flight 815 does not crash on the Island, Faraday has a different background. Daniel was allowed to pursue his passion for music, and never trained in physics. After overhearing Eloise trying to persuade Desmond to stop pursuing Penelope (Sonya Walger), Faraday approaches Desmond and shares his theory of the timeline being altered. He tells Desmond that he recently saw a red-haired woman he strongly felt he already knew and loved. Daniel states after the encounter, he made a series of notes in his journal which a mathematician has identified as advanced quantum mechanics, a topic he knows nothing about. Daniel shows his notes, and hypothesises that the world as he and Desmond are experiencing is not their correct path. Faraday then tells him Penelope is his half-sister and where Desmond can find her. Later, Faraday meets Charlotte at his benefit concert, but they do not yet realize they are in the afterlife. Daniel then takes the stage with DriveShaft to play as Charlotte watches from the crowd. It is later implied that both Eloise and Desmond are both aware that they are living in the afterlife. Eloise convinces Desmond to let Faraday live out the rest of his afterlife, since Faraday was never allowed to live the life he wanted in his past, and Eloise was never allowed to spend time with her son.

Development

After Naomi Dorrit (Marsha Thomason) landed on the island in season three, the producers began to plan who else would be on the boat she came from. They wanted these new characters to be interested in finding the island for their own personal reasons. During the casting of the "freighter folk"—the nickname that Lost's producers Damon Lindelof and Carlton Cuse use to refer to Daniel, Charlotte, Miles and Frank—fake names, occupations and scenes were temporarily assigned, to limit the leak of spoilers. In the initial casting call, Daniel was referred as "brilliant mathematician" "Russell".

Jeremy Davies was cast as Daniel because he was one of the writer-producers' favorite character actors, and they think that his "transformative quality [and] the tremendous intelligence that seems to emanate from him … seemed perfect for [the part]." The producers constructed the role around Davies based on his performances in Rescue Dawn and Solaris. When Davies met costume designer Roland Sanchez, he was wearing a thin black tie.  Sanchez merged this "cool, edgy look" with his idea for the character's clothes: a "nerdy" loosely woven dress shirt from J.Crew. Davies reportedly took a "crash course" on physics to understand the character better. Showrunners Damon Lindelof and Carlton Cuse called Daniel Faraday "an obvious shout-out to Michael Faraday, scientist and physicist". Faraday was originally planned to be a recurring role.

Reception
Producers Lindelof and Cuse were worried about how the new characters would be received by fans, after the unhappy reaction to new characters Nikki (Kiele Sanchez) and Paulo (Rodrigo Santoro), introduced in season three. However, following their introduction in "Confirmed Dead", the four characters were well received, with Paige Albiniak of the New York Post citing them as a reason behind the show's improved ratings.
IGN's Chris Carabott described Daniel, as well as the other new characters from the freighter, as "great" and "exciting". James Poniewozik of Time liked the introduction of the new characters from the freighter because "Each got just one flashback and a little time on the island, and yet by the end of the episode, [he] felt [he] had a true handle on what they were like as individuals".  Oscar Dahl of BuddyTV called it the "perfect introduction". Michael Ausiello of TV Guide also liked their introduction, and praised the actors' performances. Jeff Jensen from Entertainment Weekly liked that the "fascinating" new characters brought "mind-blowing new possibilities, and exciting new theory fodder".

Many critics praised Davies' performance and appearance. Tom Iacuzio of The Daytona Beach News-Journal deemed Jeremy Davies's performance deserving of a Primetime Emmy Award. Alan Sepinwall of The Star-Ledger claimed Davies's performance to be "outstanding" .  Jay Glatfelter of The Huffington Post said that Daniel "more and more becoming one of [his] favorite characters". Chris Carabott wrote that Davies presents Faraday's awkward mannerisms well. In a later review, Carabott commented, "I've become a huge fan of Davies over the course of the last couple of years thanks to his performance on this show." Rachel Dovey of Paste said "The Variable" revealed "a whole different" side of Daniel: "We've oscillated before about the true nature of the physicist, whether it's good or evil [...] We decided he's mostly a decent guy, barring the whole experimenting-on-his-girlfriend-then-running-away-when-her-brain-turned-to-mush thing. In the past, he's just seemed lost and confused, and, since he has those big, earnest puppy eyes, we decided to forgive him. But the episode showed us the dynamic at the heart of Daniel's stuttering vulnerability. Like all broken superheroes and Freudian beings, the man has mommy issues. This week we dove inside the dynamic between Daniel and his mother growing up." Also, Adam Sweeney believed Davies's acting was the "high point" of the episode.
A reviewer for TVoholic claimed he would have "loved any sort of explanation as to why [Daniel] changed his mind about changing the past or how he thought this could work. There must have been something that made Daniel think this was possible, but he was in such a rush that he never took care to explain."

Critics expressed shock regarding Daniel's death. David Oliver of CHUD.com felt "bummed" to see Daniel go. Dan Compora of Airlock Alpha also said the shooting of Daniel at the end was "stunning." Jon Lachonis of TVOvermind claimed that as an internal character piece, "The Variable" was "not so much a great ending for Daniel.

Jeremy Davies submitted the episode "The Constant" on his behalf for a Primetime Emmy Award for Outstanding Supporting Actor in a Drama Series.

References

Fictional characters from Massachusetts
Fictional inventors
Fictional theoretical physicists
Lost (2004 TV series) characters
Fictional musicians
Television characters introduced in 2008
Fictional University of Oxford people
Time travelers
Male characters in television

Daniel Faraday


The Klien-Lindner axle (German: Klien-Lindner-Hohlachse) is a special type of hollow driving axle on steam locomotives that enable better curve running due to its ability to slide transversely. It was developed by the German engineers, Ewald Klien and Heinrich Lindner, of the Royal Saxon State Railways (Königlich Sächsische Staatseisenbahnen).

Design features

The Klien-Lindner axle uses a double, or hollow, axle, one inside the other. It has a hollow axle (Hohlachse) on the outside, connected at its centre by a Cardan joint to a fixed driving axle running through it. The Cardan joint comprises two spherical elements that are interlinked - a solid one on the fixed axle and a hollow one on the outer hollow axle, each oriented at 90° to the other  that transfer the driving forces from the rigid axle to the hollow one. The hollow spheroid acts as a sort of link motion. In this way the hollow axle can be turned by the fixed axle. In addition, the connecting link is shaped so that the axles can slide relative to one another, parallel to their axes, to a small extent. The degree to which the hollow axle can swivel is set by the outer diameter of the fixed axle and the internal diameter of the hollow one.

This system is used on steam locomotives with fixed outer frames and coupled axles. Typically the conventionally driven wheels are in the centre and there are outer Klien-Lindner axles, front and rear. In this way the wheels, which are fixed to the hollow axles, are 'steered' by shafts that pivot on the frame when the locomotive is curve running. Coupling rods from the conventional driving wheels in the centre act on drive cranks on the inner axles fixed to the frame.

In spite of their relatively simple design Klien-Lindner axles were not widely used. Derailments were common when they were used as leading axles. The axles often caused uneven, jerky running as a result of the resistance forces that arise from this type of Cardan joint, and they were expensive to maintain, something which was not offset by the reduced wear and tear on wheel flanges and rails.

Examples

Several locomotives of this type were ordered for the Matheran Hill Railway in India, which has curves as sharp as , traversed at a speed of .  Consulting engineer Everard Calthrop designed a 0-6-0T with Klien-Lindner articulated coupled axles to provide a flexible wheelbase, and four were supplied by Orenstein & Koppel.
Steam locomotives with Klien-Lindner axle are still widely used for narrow gauge sugarcane railway in Java, Indonesia.

Locomotives with Klien-Lindner hollow axles (selection):

 BBÖ Kh
 DR Class 99.331 (Brigadelok)
 HF 210 E, a military field locomotive
 MLR Class ML,  used on the Matheran Hill Railway.
 Prussian T 37
 Nos. 1 to 3 of the Rosenberg–Korytnica branch line
 Saxon I K (some)
 Saxon V K
 Saxon XV HTV
 Saxon IX V
 GLÜCKAUF and TRUSETAL of the Trusebahn

Literature
 Deutsches Reichspatent DRP 27.892 und 68.932, 1893
 Lionel Wiener: Articulated Locomotives Kalmbach Publishing Co., Waukesha 1970

See also

 Heywood radiating axle locomotives
 Klose-Lenkwerk
 Minimum railway curve radius
 Trench railways
 Welshpool and Llanfair Light Railway steam locomotive number 19

References

External links
 English description with clear photographs and diagrams
 Hungarian locomotive of 1916
 forums.lrpresse.fr

Steam locomotive technologies
Train axles
Articulated locomotives

Klien-Lindner axle