Bias-adjusted three-step latent Markov modeling with covariates

R. Di Mari, D.L. Oberski, J.K. Vermunt

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Latent Markov models with covariates can be estimated via 1-step maximum likelihood. However, this 1-step approach has various disadvantages, such as that the inclusion of covariates in the model might alter the formation of the latent states and that parameter estimation could become infeasible with large numbers of time points, responses, and covariates. This is why researchers typically prefer performing the analysis in a stepwise manner; that is, they first construct the measurement model, then obtain the latent state classifications, and subsequently study the relationship between covariates and latent state memberships. However, such a stepwise approach yields downward-biased estimates of the covariate effects on initial state and transition probabilities. This article, shows how to overcome this problem using a generalization of the bias-corrected 3-step estimation method proposed for latent class analysis (Asparouhov & Muthén, 2014; Bolck, Croon, & Hagenaars, 2004; Vermunt, 2010). We give a formal derivation of the generalization to latent Markov models and discuss how it can be used with many time points by incorporating it into a Baum–Welch type of expectation-maximization algorithm. We evaluate the method through a simulation study and illustrate it using an application on household financial portfolio change. Our study shows that the proposed correction method yields unbiased parameter estimates and accurate standard errors, except for situations with very poorly separated classes and a small sample.
Original languageEnglish
Pages (from-to)649-660
JournalStructural Equation Modeling
Volume23
Issue number5
DOIs
Publication statusPublished - 2016

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Covariates
trend
Modeling
Markov Model
Latent Class Analysis
Parameter estimation
Maximum likelihood
Expectation-maximization Algorithm
Standard error
Transition Probability
Small Sample
Estimate
inclusion
Biased
Maximum Likelihood
Parameter Estimation
Inclusion
simulation
Simulation Study
Evaluate

Cite this

Di Mari, R. ; Oberski, D.L. ; Vermunt, J.K. / Bias-adjusted three-step latent Markov modeling with covariates. In: Structural Equation Modeling. 2016 ; Vol. 23, No. 5. pp. 649-660.
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abstract = "Latent Markov models with covariates can be estimated via 1-step maximum likelihood. However, this 1-step approach has various disadvantages, such as that the inclusion of covariates in the model might alter the formation of the latent states and that parameter estimation could become infeasible with large numbers of time points, responses, and covariates. This is why researchers typically prefer performing the analysis in a stepwise manner; that is, they first construct the measurement model, then obtain the latent state classifications, and subsequently study the relationship between covariates and latent state memberships. However, such a stepwise approach yields downward-biased estimates of the covariate effects on initial state and transition probabilities. This article, shows how to overcome this problem using a generalization of the bias-corrected 3-step estimation method proposed for latent class analysis (Asparouhov & Muth{\'e}n, 2014; Bolck, Croon, & Hagenaars, 2004; Vermunt, 2010). We give a formal derivation of the generalization to latent Markov models and discuss how it can be used with many time points by incorporating it into a Baum–Welch type of expectation-maximization algorithm. We evaluate the method through a simulation study and illustrate it using an application on household financial portfolio change. Our study shows that the proposed correction method yields unbiased parameter estimates and accurate standard errors, except for situations with very poorly separated classes and a small sample.",
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Bias-adjusted three-step latent Markov modeling with covariates. / Di Mari, R.; Oberski, D.L.; Vermunt, J.K.

In: Structural Equation Modeling, Vol. 23, No. 5, 2016, p. 649-660.

Research output: Contribution to journalArticleScientificpeer-review

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