Multivariate zero-inflated modeling with latent predictors: Modeling feedback behavior

In educational studies, the use of computer-based assessments leads to the collection of multiple outcomes to assess student performance. The student-specific outcomes are correlated and often measured in different scales, such as continuous and count outcomes. A multivariate zero-inflated model with random effects is proposed and adapted for the challenging situation where the multiple outcomes are zero-inflated and possibly right truncated. The joint model consists of a Bernoulli component to deal with the problem of extra zeros, and a multivariate truncated component to model correlated mixed response outcomes from the same subject. In a Bayesian modeling approach, MCMC methods are used for parameter estimation. Using a simulation study, it is shown that the within-individual correlation between counts can be accurately estimated together with the other model parameters. The multivariate zero-inflated model is applied to a computer-based feedback study about computer literacy, where first-year bachelor students were given the opportunity to receive additional feedback. The total number of feedback pages visited and the total feedback processing time are modeled using a Poisson and a Gamma distribution, respectively. The joint modeling framework is extended to incorporate explanatory latent variables (student performance and speed of working), to explore individual heterogeneity in feedback behavior in a computer-based assessment.

[1]  Jie Zhang,et al.  Regression models for mixed Poisson and continuous longitudinal data , 2007, Statistics in medicine.

[2]  Bernard P. Veldkamp,et al.  Effects of feedback in a computer-based assessment for learning , 2012, Comput. Educ..

[3]  C. McCulloch.  Joint modelling of mixed outcome types using latent variables , 2008, Statistical methods in medical research.

[4]  Bernard P. Veldkamp,et al.  Attention paid to feedback provided by a computer-based assessment for learning on information literacy , 2011, Comput. Educ..

[5]  Jeroen K. Vermunt,et al.  7. Multilevel Latent Class Models , 2003 .

[6]  Anthony O'Hagan,et al.  Review of Statistical Methods for Analysing Healthcare Resources and Costs , 2010, Health economics.

[7]  J. Aitchison,et al.  The multivariate Poisson-log normal distribution , 1989 .

[8]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[9]  Jim Albert,et al.  A Bayesian Analysis of a Poisson Random Effects Model for Home Run Hitters , 1992 .

[10]  Sophia Rabe-Hesketh,et al.  Generalized latent variable models: multilevel, longitudinal, and structural equation models , 2004 .

[11]  J WIM,et al.  A HIERARCHICAL FRAMEWORK FOR MODELING SPEED AND ACCURACY ON TEST ITEMS , 2007 .

[12]  Geert Molenberghs,et al.  Multiple‐Imputation‐Based Residuals and Diagnostic Plots for Joint Models of Longitudinal and Survival Outcomes , 2010, Biometrics.

[13]  Jay Magidson,et al.  Hierarchical Mixture Models for Nested Data Structures , 2004, GfKl.

[14]  R. H. Klein Entink,et al.  A Multivariate Multilevel Approach to the Modeling of Accuracy and Speed of Test Takers , 2008, Psychometrika.

[15]  J. P. Meyer,et al.  A Mixture Rasch Model With Item Response Time Components , 2010 .

[16]  C. Glas,et al.  Elements of adaptive testing , 2010 .

[17]  Jean-Paul Fox,et al.  Bayesian modeling of measurement error in predictor variables using item response theory , 2003 .

[18]  Peter E. Rossi,et al.  A Bayesian analysis of the multinomial probit model with fully identified parameters , 2000 .

[19]  Hui-ming Wang,et al.  A Bayesian multivariate Poisson regression model of cross-category store brand purchasing behavior , 2007 .

[20]  Sophia Rabe-Hesketh,et al.  Multilevel and Latent Variable Modeling with Composite Links and Exploded Likelihoods , 2007 .

[21]  Diane Lambert,et al.  Zero-inflacted Poisson regression, with an application to defects in manufacturing , 1992 .

[22]  Lijuan Wang,et al.  IRT–ZIP Modeling for Multivariate Zero-Inflated Count Data , 2010 .

[23]  Mei-Chen Hu,et al.  Zero-Inflated and Hurdle Models of Count Data with Extra Zeros: Examples from an HIV-Risk Reduction Intervention Trial , 2011, The American journal of drug and alcohol abuse.

[24]  Alan Agresti,et al.  Random effect models for repeated measures of zero-inflated count data , 2005 .

[25]  M. Croon,et al.  Predicting group-level outcome variables from variables measured at the individual level: a latent variable multilevel model. , 2007, Psychological methods.

[26]  Jean-Paul Fox,et al.  Modeling of Responses and Response Times with the Package cirt , 2007 .

[27]  van der Linden,et al.  A hierarchical framework for modeling speed and accuracy on test items , 2007 .

[28]  J. Fox.  Bayesian Item Response Modeling: Theory and Applications , 2010 .

[29]  Larry Ambrose,et al.  The power of feedback. , 2002, Healthcare executive.

[30]  Beatrijs Moerkerke,et al.  The analysis of zero-inflated count data: beyond zero-inflated Poisson regression. , 2012, The British journal of mathematical and statistical psychology.

[31]  N. Hjort,et al.  Post-Processing Posterior Predictive p Values , 2006 .

[32]  K. Wannemuehler,et al.  On the Use of Zero-Inflated and Hurdle Models for Modeling Vaccine Adverse Event Count Data , 2006, Journal of biopharmaceutical statistics.

[33]  Peter Congdon,et al.  Bayesian Models for Categorical Data , 2005 .

[34]  B. Muthén,et al.  The multilevel latent covariate model: a new, more reliable approach to group-level effects in contextual studies. , 2008, Psychological methods.

[35]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[36]  A James O'Malley,et al.  A Bayesian model for repeated measures zero-inflated count data with application to outpatient psychiatric service use , 2010, Statistical modelling.

[37]  Michel Wedel,et al.  The Structure of Self-Reported Emotional Experiences: A Mixed-Effects Poisson Factor Model , 2003, The British journal of mathematical and statistical psychology.