Content deleted Content added
Citation bot (talk | contribs) Add: s2cid, authors 1-1. Removed parameters. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by Abductive | #UCB_webform 2395/3850 |
|||
Line 56:
*'''Likelihood ratio statistic:'''<ref>Lawley, D. N. (1940). The estimation of factor loadings by the method of maximumlikelihood. Proceedings of the Royal Society ofedinborough, 60A, 64-82.</ref> Used to test the null hypothesis that a model has perfect model fit. It should be applied to models with an increasing number of factors until the result is nonsignificant, indicating that the model is not rejected as good model fit of the population. This statistic should be used with a large sample size and normally distributed data. There are some drawbacks to the likelihood ratio test. First, when there is a large sample size, even small discrepancies between the model and the data result in model rejection.<ref name =Humphreys/><ref>{{cite journal | last1 = Hakstian | first1 = A. R. | last2 = Rogers | first2 = W. T. | last3 = Cattell | first3 = R. B. | year = 1982 | title = The behavior of number-offactors rules with simulated data | journal = Multivariate Behavioral Research | volume = 17 | issue = 2| pages = 193–219 | doi = 10.1207/s15327906mbr1702_3 | pmid = 26810948 }}</ref><ref>{{cite journal|last=Harris|first=M. L.|author2=Harris, C. W.|title=A Factor Analytic Interpretation Strategy|journal=Educational and Psychological Measurement|date=1 October 1971|volume=31|issue=3|pages=589–606|doi=10.1177/001316447103100301|s2cid=143515527 }}</ref> When there is a small sample size, even large discrepancies between the model and data may not be significant, which leads to underfactoring.<ref name =Humphreys/> Another disadvantage of the likelihood ratio test is that the null hypothesis of perfect fit is an unrealistic standard.<ref name=Maccallum>{{cite journal | last1 = Maccallum | first1 = R. C. | year = 1990 | title = The need for alternative measures of fit in covariance structure modeling | journal = Multivariate Behavioral Research | volume = 25 | issue = 2| pages = 157–162 | doi=10.1207/s15327906mbr2502_2| pmid = 26794477 }}</ref><ref name=Browne>{{cite journal | last1 = Browne | first1 = M. W. | last2 = Cudeck | first2 = R. | year = 1992 | title = Alternative ways of assessing model fit | journal = Sociological Methods and Research | volume = 21 | issue = 2 | pages = 230–258 | doi = 10.1177/0049124192021002005 | s2cid = 120166447 }}</ref>
*'''Root mean square error of approximation (RMSEA) fit index:''' RMSEA is an estimate of the discrepancy between the model and the data per degree of freedom for the model. Values less that .05 constitute good fit, values between 0.05 and 0.08 constitute acceptable fit, a values between 0.08 and 0.10 constitute marginal fit and values greater than 0.10 indicate poor fit .<ref name =Browne/><ref>Steiger, J. H. (1989). EzPATH: A supplementary module for SYSTAT andsygraph. Evanston, IL: SYSTAT</ref> An advantage of the RMSEA fit index is that it provides confidence intervals which allow researchers to compare a series of models with varying numbers of factors.
*'''Information Criteria''' Information criteria such as Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC) <ref>Neath, A. A., & Cavanaugh, J. E. (2012). The Bayesian information criterion: background, derivation, and applications. Wiley Interdisciplinary Reviews: Computational Statistics, 4(2), 199-203.</ref> can be used to trade-off model fit with model complexity and select an optimal number of factors.
*'''Out-of-sample Prediction Errors''' Using the connection between model-implied covariance matrices and standardized regression weights, the best model can be selected using out-of-sample prediction errors.<ref>Haslbeck, J., & van Bork, R. (2022). Estimating the number of factors in exploratory factor analysis via out-of-sample prediction errors. Psychological Methods.</ref>
===Optimal Coordinate and Acceleration Factor===
| |||