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Monte Carlo simulation reveals standard asymptotic theory fails without regularity conditions in factor models, highlighting risks of standard goodness-of-fit testing.
The use of the likelihood ratio statistic in testing the goodness of fit of the exploratory factor model has no formal justification when, as is often the case in practice, the usual regularity conditions are not met. In a Monte Carlo experiment it is found that the asymptotic theory seems to be appropriate when the regularity conditions obtain and sample size is at least 30. When the regularity conditions are not satisfied, the asymptotic theory seems to be misleading in all sample sizes considered.
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Geweke et al. (1980) studied this question.
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