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A Latent Transition Analysis Model for Latent-State-Dependent Nonignorable Missingness

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Abstract

Psychologists often use latent transition analysis (LTA) to investigate state-to-state change in discrete latent constructs involving delinquent or risky behaviors. In this setting, latent-state-dependent nonignorable missingness is a potential concern. For some longitudinal models (e.g., growth models), a large literature has addressed extensions to accommodate nonignorable missingness. In contrast, little research has addressed how to extend the LTA to accommodate nonignorable missingness. Here we present a shared parameter LTA that can reduce bias due to latent-state-dependent nonignorable missingness: a parallel-process missing-not-at-random (MNAR-PP) LTA. The MNAR-PP LTA allows outcome process parameters to be interpreted as in the conventional LTA, which facilitates sensitivity analyses assessing changes in estimates between LTA and MNAR-PP LTA. In a sensitivity analysis for our empirical example, previous and current membership in high-delinquency states predicted adolescents’ membership in missingness states that had high nonresponse probabilities for some or all items. A conventional LTA overestimated the proportion of adolescents ending up in a low-delinquency state, compared to an MNAR-PP LTA.

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Notes

  1. The LTA model is also known as a multiple-indicator latent Markov model (e.g., Langeheine & Van de Pol, 1990).

  2. The \(Q=1\) state model necessarily has a different structure; it simply consists of estimating a set of missingness indicator thresholds for that single class.

  3. Suppose the MNAR-SP LTA results indicated that a particular state at time \(t\) evidenced a high probability of violent behavior and a high probability of missingness. Persons might obtain a similarly high posterior probability of assignment to that MNAR-SP LTA state simply by endorsing many aggressive items (even if they had no missingness), or by having many missing responses (even if they endorsed no aggressive items). Yet, substantively, researchers would want to be able to distinguish among such persons.

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  1. Quantitative Methods Program, Department of Psychology and Human Development, Vanderbilt University, Peabody #552, 230 Appleton Place, Nashville, TN, 37203 , USA

    Sonya K. Sterba

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Sterba, S.K. A Latent Transition Analysis Model for Latent-State-Dependent Nonignorable Missingness. Psychometrika 81, 506–534 (2016). https://doi.org/10.1007/s11336-015-9442-4

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