We examine the accuracy of p values obtained using the asymptotic mean and variance (MV) correction to the distribution of the sample standardized root mean squared residual (SRMR) proposed by Maydeu-Olivares to assess the exact fit of SEM models. In a simulation study, we found that under normality, the MV-corrected SRMR statistic provides reasonably accurate Type I errors even in small samples and for large models, clearly outperforming the current standard, that is, the likelihood ratio (LR) test. When data shows excess kurtosis, MV-corrected SRMR p values are only accurate in small models ( p = 10), or in medium-sized models ( p = 30) if no skewness is present and sample sizes are at least 500. Overall, when data are not normal, the MV-corrected LR test seems to outperform the MV-corrected SRMR. We elaborate on these findings by showing that the asymptotic approximation to the mean of the SRMR sampling distribution is quite accurate, while the asymptotic approximation to the standard deviation is not.

We introduce a novel, regression-based moderation framework to model faking effects that incorporates evaluation of faking tendency as a moderator. We also consider how perceived trait desirability may be factored into the framework and provide programming code for applied researchers to utilize the method in their research. Using this framework, we revisit a well-known response format (i.e., forced-choice) to formally evaluate its ability to mitigate the effects of applicant faking as compared to the widely used Likert format. The impetus for the latter evaluation stems from the use of item response theory (IRT) modeling to yield non-ipsative scores from forced-choice measures. We found strong support for the need to incorporate moderating effects of faking tendency and desirability in predicting applicants’ responses. Also, we found that the only substantial difference across formats lies in forced-choice scores yielding a lower mean inflation at high faking values. As a result, forced-choice scores do not outperform Likert scores when selection ratios are used but may be beneficial when cutoff scores are used. Application of the moderation framework presented extends to self-reported construct measures of varied kinds.

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