# Factor Analysis

If we make the assumption that a set of underlying (or latent) variables is responsible for a large part of the dynamics in the target dataset, then we can use a set of techniques that seek to identify and quantify those underlying variables. While many such techniques exist, one such very widely used one is called Factor Analysis. Rotation Options:

• None
• Equamax
• Orthomax
• Parsimax
• Promax
• Quartimax
• Varimax

Scoring:

• WLS
• Regression

N : Number of Components

### Description#

The factor analysis model can be described as $$Y = \Lambda F + E$$ where
$\Lambda$ are the factor weights
$F$ are the factor scores
$E$ is the error term

Clearly, a reconstructed approximation of the target dataset can be carried out by $\Lambda * F$. For example, in a single factor model:

$$\begin{matrix} y_1 = \lambda_{1} f_{1} + \epsilon_{1} \\ y_2 = \lambda_{2} f_{1} + \epsilon_{2} \\ y_3 = \lambda_{3} f_{1} + \epsilon_{3} \end{matrix}$$

### Returns#

• GoF: Chi-square, p-value, log-likelihood
• Factor Loadings: $\Lambda\$ i.e. weights
• Rotation Matrix
• Factor Scores: $F$
• MLE Variances:
{"ft_lang_label":"__label__en","ft_lang_prob":0.736408,"math_prob":0.99750787,"size":1115,"snap":"2022-40-2023-06","text_gpt3_token_len":311,"char_repetition_ratio":0.10711071,"word_repetition_ratio":0.0,"special_character_ratio":0.29506725,"punctuation_ratio":0.098958336,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99995756,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-03T09:09:21Z\",\"WARC-Record-ID\":\"<urn:uuid:8438e4b7-50df-4560-b5ed-ecab472f5bfd>\",\"Content-Length\":\"14971\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b321ae8d-5df6-4678-b334-b793abd3ce1f>\",\"WARC-Concurrent-To\":\"<urn:uuid:a2719c63-2096-4444-a14a-4e9530aec3e8>\",\"WARC-IP-Address\":\"35.231.208.25\",\"WARC-Target-URI\":\"https://docs.pnumerics.com/docs/decomposition/factan/\",\"WARC-Payload-Digest\":\"sha1:WZD45O5QZZNR5EPSPCQZZDFFAFL4WDUV\",\"WARC-Block-Digest\":\"sha1:SKXKXMMJM42VP67DN4ZILRTKBGS2EWJE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337404.30_warc_CC-MAIN-20221003070342-20221003100342-00773.warc.gz\"}"}