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Validity of the chi‐square test in dichotomous variable factor analysis when expected frequencies are small
Author(s) -
Reiser Mark,
VandenBerg Maria
Publication year - 1994
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1994.tb01026.x
Subject(s) - statistics , mathematics , goodness of fit , type i and type ii errors , monte carlo method , test statistic , statistic , chi square test , variable (mathematics) , statistical hypothesis testing , econometrics , mathematical analysis
This paper presents a comparison of results from two methods for estimating and testing a model for the factor analysis of dichotomous variables. For k manifest dichotomous variables, the data can be cross‐classified to form a vector of 2 k frequencies, and nonlinear methods that use the full information in these 2 k frequencies are available for factor analysis. In addition, another method that uses only the limited information in the first‐, and second‐order marginal frequencies is available for the same model. As k becomes larger, substantial differences between the full‐information and limited‐information methods become apparent in results from the test of fit. For large k . Type I and Type II error rates may be higher in the full‐information approach, because as the vector of 2 k frequencies becomes sparse, the chi‐square approximation for the distribution of the goodness‐of‐fit test statistic becomes poorer. In this paper, Monte Carlo experiments are used under a variety of conditions to compare the methods for rate of Type I errors when the model matches the simulated data and for the rate of Type II errors when the model does not match the simulated data.