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.

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We consider models which combine latent class measurement models for categorical latent variables with structural regression models for the relationships between the latent classes and observed explanatory and response variables. We propose a two-step method of estimating such models. In its first step, the measurement model is estimated alone, and in the second step the parameters of this measurement model are held fixed when the structural model is estimated. Simulation studies and applied examples suggest that the two-step method is an attractive alternative to existing one-step and three-step methods. We derive estimated standard errors for the two-step estimates of the structural model which account for the uncertainty from both steps of the estimation, and show how the method can be implemented in existing software for latent variable modelling.

Latent class analysis is used in the political science literature in both substantive applications and as a tool to estimate measurement error. Many studies in the social and political sciences relate estimated class assignments from a latent class model to external variables. Although common, such a “three-step” procedure effectively ignores classification error in the class assignments; Vermunt (2010, “Latent class modeling with covariates: Two improved three-step approaches,” Political Analysis 18:450–69) showed that this leads to inconsistent parameter estimates and proposed a correction. Although this correction for bias is now implemented in standard software, inconsistency is not the only consequence of classification error. We demonstrate that the correction method introduces an additional source of variance in the estimates, so that standard errors and confidence intervals are overly optimistic when not taking this into account. We derive the asymptotic variance of the third-step estimates of interest, as well as several candidate-corrected sample estimators of the standard errors. These corrected standard error estimators are evaluated using a Monte Carlo study, and we provide practical advice to researchers as to which should be used so that valid inferences can be obtained when relating estimated class membership to external variables.

Personal growth initiative (PGI), defined as being proactive about one's personal development, is critical to graduate students' academic success. Prior research has shown that students' PGI can be enhanced through interventions that focus on stimulating developmental activities. Within this study, we aimed to investigate whether an intervention that stimulates development in the area of one's personal strengths (strengths intervention) has more beneficial effects on students' PGI than an intervention that stimulates development in the area of individual deficiencies (deficiency intervention). We conducted 2 longitudinal field experiments to investigate the effects of the 2 interventions on students' PGI (Experiment 1) and the potential mediating role of psychological capital (PsyCap) in this regard (Experiment 2). In Experiment 1, 105 (N = 105) university students participated in either a strengths intervention or a deficiency intervention. Results indicated that the strengths intervention increased the students' PGI in the short but not in the long term, whereas the deficiency intervention did not affect PGI. Ninety students (N = 90) participated in Experiment 2, in which we slightly refined both interventions by putting a stronger emphasis on the ongoing development of strengths (strengths intervention) or correction of deficiencies (deficiency intervention) by adding posttraining assignments. Results suggested that participating in both interventions led to increases in PGI over a 3-month period, but that these increases were bigger for the strengths intervention group. Furthermore, the relationship between the strengths intervention and PGI was mediated by hope as one component of PsyCap.