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Mariahmcd11 (talk | contribs) |
The random-effects assumption (i.e., orthogonality to regressors) was not mentioned. Ironically! (it is often overlooked and if violated makes the estimator inconsistent--estimates will not converge to true values asymptotically). |
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;Independence of observations
Independence is an assumption of general linear models, which states that cases are random samples from the population and that scores on the dependent variable are independent of each other.<ref name="Green">{{cite book|last=Salkind|first=Samuel B. Green, Neil J.|title=Using SPSS for Windows and Macintosh : analyzing and understanding data|year=2004|publisher=Pearson Education|___location=Upper Saddle River, NJ|isbn=978-0-13-146597-8|edition=4th|url-access=registration|url=https://archive.org/details/usingspssforwind00samu}}</ref> One of the main purposes of multilevel models is to deal with cases where the assumption of independence is violated; multilevel models do, however, assume that 1) the level 1 and level 2 residuals are uncorrelated and 2) The errors (as measured by the residuals) at the highest level are uncorrelated.<ref>{{cite web |title=Introduction to Multilevel Modeling Using HLM 6 |author=ATS Statistical Consulting Group |url=http://www.ats.ucla.edu/stat/hlm/seminars/hlm6/outline_hlm_seminar.pdf |archive-date=31 December 2010 |archive-url=https://web.archive.org/web/20101231163641/http://www.ats.ucla.edu/stat/hlm/seminars/hlm6/outline_hlm_seminar.pdf }}</ref>
;Orthogonality of regressors to random effects
The regressors must not correlate with the random effects, <math>u_{0j}</math>. This assumption is testable but often ignored, rendering the estimator inconsistent<ref name=":0">{{Cite journal |last=Antonakis |first=John |last2=Bastardoz |first2=Nicolas |last3=Rönkkö |first3=Mikko |date=2021 |title=On Ignoring the Random Effects Assumption in Multilevel Models: Review, Critique, and Recommendations |url=http://journals.sagepub.com/doi/10.1177/1094428119877457 |journal=Organizational Research Methods |language=en |volume=24 |issue=2 |pages=443–483 |doi=10.1177/1094428119877457 |issn=1094-4281}}</ref>. If this assumption is violated, the random-effect must be modeled explicitly in the fixed part of the model, either by using dummy variables or including cluster means of all <math>X_{ij} </math> regressors<ref name=":0" /><ref>{{Cite journal |last=McNeish |first=Daniel |last2=Kelley |first2=Ken |date=2019 |title=Fixed effects models versus mixed effects models for clustered data: Reviewing the approaches, disentangling the differences, and making recommendations. |url=http://doi.apa.org/getdoi.cfm?doi=10.1037/met0000182 |journal=Psychological Methods |language=en |volume=24 |issue=1 |pages=20–35 |doi=10.1037/met0000182 |issn=1939-1463}}</ref><ref>{{Cite journal |last=Bliese |first=Paul D. |last2=Schepker |first2=Donald J. |last3=Essman |first3=Spenser M. |last4=Ployhart |first4=Robert E. |date=2020 |title=Bridging Methodological Divides Between Macro- and Microresearch: Endogeneity and Methods for Panel Data |url=http://journals.sagepub.com/doi/10.1177/0149206319868016 |journal=Journal of Management |language=en |volume=46 |issue=1 |pages=70–99 |doi=10.1177/0149206319868016 |issn=0149-2063}}</ref>. This assumption is probably the most important assumption the estimator makes, but one that is misunderstood by most applied researchers using these types of models<ref name=":0" />.
==Statistical tests==
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