Missing data mechanisms and their implications on the analysis of categorical data

Abstract

We review some issues related to the implications of different missing data mechanisms on statistical inference for contingency tables and consider simulation studies to compare the results obtained under such models to those where the units with missing data are disregarded. We confirm that although, in general, analyses under the correct missing at random and missing completely at random models are more efficient even for small sample sizes, there are exceptions where they may not improve the results obtained by ignoring the partially classified data. We show that under the missing not at random (MNAR) model, estimates on the boundary of the parameter space as well as lack of identifiability of the parameters of saturated models may be associated with undesirable asymptotic properties of maximum likelihood estimators and likelihood ratio tests; even in standard cases the bias of the estimators may be low only for very large samples. We also show that the probability of a boundary solution obtained under the correct MNAR model may be large even for large samples and that, consequently, we may not always conclude that a MNAR model is misspecified because the estimate is on the boundary of the parameter space.

Multiple Imputation for Dichotomous MNAR Items Using Recursive Structural Equation Modeling With Rasch Measures as Predictors

“…The highest percentage of missing values in this study was 30% for one of the variables, and the sample size of 358 was judged to be adequate to estimate the missing data. When utilizing IBM Amos, Bayesian analysis is conducted for ordered categorical data and the Markov Chain Monte Carlo (MCMC) algorithm is employed to draw random values of the parameters from joint posterior distributions (Arbuckle, 2014b;Grace, 2015;Poleto, Singer, & Paulino, 2011). When dichotomous variables are used in an Amos model, additional constraints must be added to identify the model (Arbuckle, 2014a;Grace, 2015;IBM, 2015).…”

A two‐part mixed‐effects pattern‐mixture model to handle zero‐inflation and incompleteness in a longitudinal setting

“…with dropouts and/or sporadic missing observations (see e.g. Rizopoulos et al, 2008; Alfò and Maruotti, 2009; Harel and Schafer, 2009; Tsonaka et al, 2009; Lin et al, 2010; Poleto et al, 2011). Of course, different mechanisms of missingness can be considered.…”

Análise de dados categorizados com omissão em variáveis explicativas e respostas

“…Poleto, Singer & Paulino (2011a) ilustram essa perda de informação quando há interesse em se comparar a precisão de testes diagnósticos e mostram que mesmo num caso em que o mecanismo MCARé plausível, as conclusões obtidas na ACC, e outras análises que não levam em conta toda a informação disponível, podem ser equivocadas. Além de exemplificar esse fato, Poleto, Singer & Paulino (2011b) apresentam exceções em que, para algumas funções paramétricas de interesse, os estimadores obtidos na ACC podem ser (1) consistentes sob um mecanismo MAR e (2) tão eficientes quanto os do verdadeiro mecanismo MCAR.…”

“…Molenberghs, Goetghebeur, Lipsitz & Kenward (1999), Clarke (2002) e Clarke & Smith (2004) também discutem essas patologias. Por meio de um estudo de simulação, Poleto et al (2011b) mostraram que, tanto no caso de as estimativas de ψ estarem na fronteira do espaço paramétrico quanto no caso de falta de identificabilidade, os estimadores de máxima verossimilhança são enviesados, embora com viés menor do que aquele obtido sob a ACC se o mecanismo MNAR proposto for verdadeiro. Esses autores também mostraram que a obtenção de estimativas na fronteira do espaço paramétrico nãoé um indício de que o mecanismo de omissão seja falso e, dependendo da estrutura para o mecanismo de omissão, pode ainda ocorrer com probabilidade razoável para amostras grandes (e.g., probabilidade de 18% para n = 10 000).…”