(meaning that all groups have the same values, although in the real world this would be a rare occurrence), non-randomly varying (meaning that the intercepts and/or slopes are predictable from an independent variable at Level 2), or randomly varying (meaning that the intercepts and/or slopes are different in the different groups, and that each have their own overall mean and variance). When there are multiple level 1 independent variables, the model can be expanded by substituting vectors and matrices in the equation. When the relationship between the response and predictor can not be described by the linear relationship, then one can find some non linear functional relationship between the response and predictor, and extend the model to nonlinear mixed-effects model. For example, when the response is the cumulative infection trajectory of the -th country, and represents the -th time points, then the ordered pair for each country may show a shape similar to logistic function. Level 2 regression equation The dependent variables are the intercepts and the slopes for the independent variables at Level 1 in the groups of Level 2. refers to the overall intercept. This is the grand mean of the scores on the dependent variable across all the groups when all the predictors are equal to 0. refers to the overall regression coefficient, or the slope, between the dependent variable and the Level 2 predictor. refers to the deviation of case i from the overall intercept. refers to the overall regression coefficient, or the slope, between the dependent variable and the Level 1 predictor. Types of models Before conducting a multilevel model analysis, a researcher must decide on several aspects, including which predictors are to be included in the analysis, if any. Second, the researcher must decide whether parameter values (i.e., the elements that will be estimated) will be fixed or random. Fixed parameters are composed of a constant over all the groups, whereas a random parameter has a different value for each of the groups. Additionally, the researcher must decide whether to employ a maximum likelihood estimation or a restricted maximum likelihood estimation type. Random intercepts model A random intercepts model is a model in which intercepts are allowed to vary, and therefore, the scores on the dependent variable for each individual observation are predicted by the intercept that varies across groups. This model assumes that slopes are fixed (the same across different contexts). In addition,