Is Parceling Really Necessary? A Comparison of Results From Item Parceling and Categorical Variable Methodology

Abstract

This study examined the efficacy of 4 different parceling methods for modeling categorical data with 2, 3, and 4 categories and with normal, moderately nonnormal, and severely nonnormal distributions. The parceling methods investigated were isolated parceling in which items were parceled with other items sharing the same source of variance, and distributed parceling in which items were parceled with items influenced by different factors. These parceling strategies were crossed with strategies in which items were either parceled with similarly distributed or differently distributed items, to create 4 different parceling methods. Overall, parceling together items influenced by different factors and with different distributions resulted in better model fit, but high levels of parameter estimate bias. Across all parceling methods, parameter estimate bias ranged from 20% to over 130%. Parceling strategies were contrasted with use of the WLSMV estimator for categorical, unparceled data. Results based on this estimator are encouraging, although some bias was found when high levels of nonnormality were present. Values of the chi-square and root mean squared error of approximation based on WLSMV also resulted in Type II error rates for misspecified models when data were severely nonnormally distributed.

Notes

¹Although the latter level of nonnormality is quite high, similar values of kurtosis can occur for situations in which a ceiling or floor effect is present, or for scales measuring infrequently endorsed behaviors.

²The categorical data were also fit to misspecified models to examine the power of the WLSMV estimator. This is described in more detail in a later section.

³The number of parameters was reduced by 32 for the categorical data because measurement error variances for indicators are not estimated in this model.

^aModel 1: two subfactors equally correlated with F4; Model 2: two subfactors unequally correlated with F4.

^bModel 3: Method factor correlated with F4; Model 4: method factor uncorrelated with F4.

^aModel 1: two subfactors equally correlated with F4; Model 2: two subfactors unequally correlated with F4; Model 3: method factor correlated with F4; Model 4: method factor uncorrelated with F4.

^bParcel type 1: distributed parceling, same distribution; Parcel type 2: distributed parceling, different distributions; Parcel type 3: isolated parceling, same distribution; Parcel type 4: isolated parceling, different distributions.

^aSample sizes are shown in parentheses only for chi-square; sample sizes are the same for RMSEA and CFI.