All-nothing latent class analysis for binary data: cross-sectional and longitudinal organizational research applications

Abstract This paper formalizes and extends Goodman’s (J Am Stat Assoc 70(352):755–768, 1975) all-nothing Latent Class Analysis (LCA) to accommodate data with substantial proportions of respondents that endorse either all or none of the binary indicator variables. A simulation study compares all-nothing LCA to unrestricted LCA in terms of recovering the true number of latent classes under varying sample distributions. We apply both LCA model specifications to two previously published empirical datasets having all-zero and all-one response patterns: cross-sectional study-skill indicators and binary indicators for post-retirement employment status at multiple measurement occasions. The longitudinal application of all-nothing LCA is a latent trajectory analysis that mimics the mover–stayer latent Markov model. This paper illustrates for which data patterns all-nothing constraints improve class recovery and interpretation. We conclude with recommendations and future research directions for applying all-nothing LCA in combination with unrestricted LCA.