The Impact of Item Parceling on Structural Parameter Invariance in Multi-group Structural Equation Modeling

ABSTRACT

Item parcels are the indicators of a factor which are created by summing or averaging scores of individual items. Item parceling has been widely applied in structural equation modeling (SEM) but has been less discussed in the multi-group context, especially for structural parameter invariance. The present study investigated the effect of item parceling on parameter bias and invariance tests at the structural level (i.e., latent means and a structural path) in multi-group SEM using a Monte Carlo simulation study. The results show that under a correctly specified measurement invariance model, indicator type would not introduce bias in structural parameter estimates. The estimation and statistical decision would depend on the assumption for measurement (non-)invariance and testing method, rather than the indicator type. When falsely assuming measurement invariance, latent mean or structural path differences are likely to be biased and to conclude incorrect statistical decisions in testing.

KEYWORDS:

• Item parceling
• structural equation modeling
• measurement invariance
• structural invariance

Notes

¹ Plummer (2000) found that among 100 studies using CFA, 54 studies used item parcels to test the models from 1996 to 1999. Bandalos and Finney (2001) conducted a review from 1989 to 2001 and found that 19.6% of studies used any form of item parcels among 317 applied CFA or SEM studies. Williams and O’Boyle (2008) reviewed five journals from 2001 to 2007 and found that 44% of 75 SEM studies employed an item parceling strategy.

² Detailed mathematical explanations about how item parceling reduces residual variances and, as a result, increases communalities and model fit are provided in Little et al. (2013).

³ A search was done using the terms “item parcel” or “item parceling” in the APA PsycArticles database for publications in the last twenty years. The results showed that 25 papers in which these terms appeared were published between 2001 and 2005, 68 papers between 2006 and 2010, 95 papers between 2011 and 2015, and 104 papers between 2016 and 2020.

⁴ Meade and Kroustalis (2006) only used LRT to test measurement invariance using items and item parcels.

⁵ Having twelve indicators per factor has been found from several previous simulation studies related to item parceling (Bandalos, 2002; Marsh et al., 1998; Rhemtulla, 2016). We wanted to represent cases where the number of items per factor could warrant item parcels given the number of parameters to estimate.

⁶ Making three parcels per latent factor has been recommended to make each factor model just-identified (Little et al., 2002, 2013; Marsh et al., 1998; Matsunaga, 2008). Thus, the model fit represents that of the structural model.

⁷ https://osf.io/f37wm/?view_only=16ce4f52edce4d288ba6de846749cc8c

⁸ The non-invariant items can also be seen as the indicators that share an unmodeled secondary factor (Hall et al., 1999).