Maximum likelihood estimation in the logistic regression model with a cure fraction

Diop, Aba; Diop, Aliou; Dupuy, Jean‐François

doi:10.1214/11-ejs616

Cited by 36 publications

(23 citation statements)

References 18 publications

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“…Diop, Diop and Dupuy (2011) proved the model identifiability for the zero-inflated binary regression with at least one continuous covariate. Using a similar technique, we can prove our model identifiability.…”

Section: Model Identifiability and Test For Zero Inflationmentioning

confidence: 97%

“…Min and Agresti (2002) reviewed various statistical models incorporating zero inflation in both discrete and continuous outcomes for cross-sectional data. Diop, Diop and Dupuy (2011) discussed cross-sectional binary regression with zero inflation, and proved the model identifiability when at least one covariate is continuous. Hall (2000) first considered longitudinal or clustered data with zero-inflated binomial or Poisson outcomes.…”

Section: Introductionmentioning

confidence: 99%

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Mixed model and estimating equation approaches for zero inflation in clustered binary response data with application to a dating violence study

et al. 2015

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The NEXT Generation Health study investigates the dating violence of adolescents using a survey questionnaire. Each student is asked to affirm or deny multiple instances of violence in his/her dating relationship. There is, however, evidence suggesting that students not in a relationship responded to the survey, resulting in excessive zeros in the responses. This paper proposes likelihood-based and estimating equation approaches to analyze the zero-inflated clustered binary response data. We adopt a mixed model method to account for the cluster effect, and the model parameters are estimated using a maximum-likelihood (ML) approach that requires a Gaussian–Hermite quadrature (GHQ) approximation for implementation. Since an incorrect assumption on the random effects distribution may bias the results, we construct generalized estimating equations (GEE) that do not require the correct specification of within-cluster correlation. In a series of simulation studies, we examine the performance of ML and GEE methods in terms of their bias, efficiency and robustness. We illustrate the importance of properly accounting for this zero inflation by reanalyzing the NEXT data where this issue has previously been ignored.

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Section: Model Identifiability and Test For Zero Inflationmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Mixed model and estimating equation approaches for zero inflation in clustered binary response data with application to a dating violence study

et al. 2015

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show abstract

“…Secondly, to avoid numerical issues, cautions should be taken regarding the variables included in the logit of the inflated probabilities. For example, it has been suggested that at least one of the covariates included in the regular Poisson part needs to be excluded from the logit for the zero inflation for a ZIP model, or vice versa, to prevent the possible numerical difficulties (Diop, Diop, & Dupuy, 2011;Staub & Winkelmann, 2013). For a Zero-Inflated Multinomial model, Diallo et al (2017) proposed to run a variable selection using a Logistic model for a binary indicator of whether the response is zero, and then use the resulting variables as candidates for the logit of zero-inflated probability.…”

Section: Resultsmentioning

confidence: 99%

Generalized Inflated Discrete Models: A Strategy to Work with Multimodal Discrete Distributions

Cai¹,

Xia²,

Zhou³

2017

Preprint

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W o r k i n g P a p e rAnalysts of discrete data often face the challenge of managing the tendency of inflation on certain values. When treated improperly, such phenomenon may lead to biased estimates and incorrect inferences. This study extends the existing literature on single value inflated models, and develops a general framework to handle variables with more than one inflated value. To assess the performance of the proposed maximum likelihood estimator, we conducted Monte Carlo experiments under several scenarios for different levels of inflated probabilities under Multinomial, Ordinal, Poisson, and ZeroTruncated Poisson outcomes with covariates. We found that ignoring the inflations leads to substantial bias and poor inference of the inflations-not only for the intercept(s) of the inflated categories, but other coefficients as well. Specifically, higher values of inflated probabilities are associated with larger biases. By contrast, the Generalized Inflated Discrete Models (GIDM) perform well with unbiased estimates and satisfactory coverages even when the number of parameters that need to be estimated is quite large. We showed that model fit criteria, such as AIC, could be used in selecting the appropriate specifications of inflated models. Lastly, the GIDM was implemented using large-scale health survey data as a comparison to conventional modeling approaches such as various Poisson and Ordered Logit models. We showed that the GIDM fits the data better in generalThe current work provides a practical approach to analyzing multimodal data that exists in many fields, such as heaping in self-reported behavioral outcomes, inflated categories of indifference and neutral in attitude surveys, large amounts of zero, and low occurrences of delinquent behaviors.

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“…The consistency and asymptotic normality of ψ n have been established by Diop et al (2011). Moreover, Diop et al (2011) have proved that the asymptotic covariance matrix…”

Section: Accepted Manuscriptmentioning

confidence: 97%

“…Diop et al (2011) recently established the consistency and asymptotic normality of the MLE in a ZIB model with logit links for both the response variable and the zero-inflation component.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Simulation-based Inference in a Zero-inflated Bernoulli Regression Model

Diop

Dupuy

2014

Communications in Statistics - Simulation and Computation

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Maximum likelihood estimation in the logistic regression model with a cure fraction

Cited by 36 publications

References 18 publications

Mixed model and estimating equation approaches for zero inflation in clustered binary response data with application to a dating violence study

Mixed model and estimating equation approaches for zero inflation in clustered binary response data with application to a dating violence study

Generalized Inflated Discrete Models: A Strategy to Work with Multimodal Discrete Distributions

Simulation-based Inference in a Zero-inflated Bernoulli Regression Model

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