Estimating the Association between Latent Class Membership and External Variables Using Bias-adjusted Three-step Approaches

Abstract

Latent class analysis is a clustering method that is nowadays widely used in social science research. Researchers applying latent class analysis will typically not only construct a typology based on a set of observed variables but also investigate how the encountered clusters are related to other, external variables. Although it is possible to incorporate such external variables into the latent class model itself, researchers usually prefer using a three-step approach. This is the approach wherein after establishing the latent class model for clustering (step 1), one obtains predictions for the class membership scores (step 2) and subsequently uses these predicted scores to assess the relationship between class membership and other variables (step 3). Bolck, Croon, and Hagenaars (2004) showed that this approach leads to severely downward-biased estimates of the strength of the relationships studied in step 3. These authors and later also Vermunt (2010) developed Downloaded from methods to correct for this bias. In the current study, we extended these correction methods to situations where class membership is not predicted but used as an explanatory variable in the third step, a situation widely encountered in social science applications. A simulation study tested the performance of the proposed correction methods, and their practical use was illustrated with real data examples. The results showed that also when the latent class variable is used as a predictor of external variables, the uncorrected three-step approach leads to severely biased estimates. The proposed correction methods perform well under conditions encountered in practice.

A General 3-Step Maximum Likelihood Approach to Estimate the Effects of Multiple Latent Categorical Variables on a Distal Outcome

“…Asparouhov & Muthén, 2014a;Vermunt, 2010) or a predictor of an outcome (e.g. Bakk, Tekle, & Vermunt, 2013;. Of these two extensions, the latter is of particular interest in life-course research where questions of interest include how childhood circumstances influence later life outcomes such as overall well-being.…”

“…There are three main advantages of the 1-step approach. First, it is more efficient compared to step-wise approaches that may introduce additional uncertainty between steps; second it allows for more flexible model structures, such as models with direct effects of covariates on indicators and the distal outcome; and, third, it is straightforward to account for residual correlation between Z and U s, beyond that captured by class membership (Bakk et al, 2013). However, the 1-step approach has received criticism over the past ten years regarding the practicality of the simultaneous estimation and the requirement for additional distributional assumptions about Z.…”

“…If there are multiple distal outcomes, the shift in the latent class proportions can be severe, especially when the classes outnumber the indicators or when class separation is poor. Moreover, by treating Z as an indicator for C, the 1-step approach requires additional assumptions and, for continuous Z, that Z is normally distributed within classes (Asparouhov & Muthén, 2014a;Bakk et al, 2013;.…”

“…The consideration of such an extension was first suggested by Bolck et al (2004). Bakk et al (2013) also discussed briefly an application of the 3-step maximum likelihood (ML) approach with two latent categorical variables where one predicts the other. Our proposed model has a more flexible specification that allows for an association between the latent variables through a log-linear model.…”

Some suggestions on dealing with measurement error in linkage analyses

“…In Bachl and Scharkow (2017), we used a more elaborated least squares procedure with equality and inequality constraints (lsei() from the limSolve package; Soetaert, Van den Meersche, & van Oevelen, 2009) to guarantee corrected proportions inside the range between 0 and 1. Similar correction procedures are implemented in Mplus (Asparouhov & Muthén, 2014) and Latent Gold (Bakk, Tekle, & Vermunt, 2013), where they are used in the context of latent class analysis. They could also be adapted to correct the estimated proportions from the content analysis part of a linkage study given the observed data and an approximation of the misclassification probabilities.…”