Random effects probit and logit: understanding predictions and marginal effects

Bland, James R.; Cook, Amanda

doi:10.1080/13504851.2018.1441498

Cited by 31 publications

(20 citation statements)

References 6 publications

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“…We used a probit model ( xtprobit command) with robust clustered standard errors at the individual level. To aid interpretation of the relationships between the explanatory variables and adherence, we estimated average adjusted probabilities [ 45 ] of the clinic and caregiving factors that were statistically significant in the multivariable regression ( P < 0.05), using margins and lincom commands [ 46 ].…”

Section: Methodsmentioning

confidence: 99%

Clinic and care: associations with adolescent antiretroviral therapy adherence in a prospective cohort in South Africa

Cluver

Shenderovich

Toska

et al. 2021

Aids

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Section: Methodsmentioning

confidence: 99%

Clinic and care: associations with adolescent antiretroviral therapy adherence in a prospective cohort in South Africa

Cluver

Shenderovich

Toska

et al. 2021

Aids

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“…A substantial literature in the social sciences has addressed the problem of coefficient comparison across groups in non-linear probability models, probit and logit, on the basis of unobserved heterogeneity, beginning with the seminal 1999 paper of Allison [ 80 ]. We do not pursue this theme [ 81 ] further, rather, submit that coefficient non-concordance is a function of the well described non-collapsibility of both odds ratios and probit regression coefficients [ 56 , 82 ] and may be suitably resolved using marginal effects, including effect derivatives, on the probability scale [ 16 , 83 ]: “… the output from non-linear models must be converted into marginal effects to be useful. Marginal effects are the (average) changes in the CEF [conditional expectation function: the expectation, or population average, of Y i (dependent variable) with X i (covariate vector) held fixed] implied by a non-linear model.…”

Section: Discussionmentioning

confidence: 99%

“…This ignores the fact that both risk differences and risk RR are collapsible metrics, as opposed to OR and probit coefficients. In Stata™, the “margins” command, introduced in Version 11 (July 2009), is a seamlessly integrated post-estimation tool, albeit it has undergone relevant computational revisions [ 16 ].…”

Section: Discussionmentioning

confidence: 99%

“…Model validation has also differed between disciplines. Within the biomedical and epidemiological literature extensive discussion has focused around concepts of discrimination and calibration [ 11 – 13 ], whereas in econometrics bias and parameter consistency have been dominant [ 14 – 16 ], to the exclusion of model performance issues such as goodness-of-fit [ 17 ], although some issues intersect [ 18 ]. Econometrics has paid greater attention to concepts such as endogeneity [ 19 ], self-selection [ 20 ] and non-randomized treatment assignment [ 21 ], although there has been a rapid increase in the biomedical literature devoted to these issues, especially in epidemiology [ 22 ].…”

Section: Introductionmentioning

confidence: 99%

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Modelling hospital outcome: problems with endogeneity

Moran

Santamaria

Duke

2021

BMC Med Res Methodol

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Background Mortality modelling in the critical care paradigm traditionally uses logistic regression, despite the availability of estimators commonly used in alternate disciplines. Little attention has been paid to covariate endogeneity and the status of non-randomized treatment assignment. Using a large registry database, various binary outcome modelling strategies and methods to account for covariate endogeneity were explored. Methods Patient mortality data was sourced from the Australian & New Zealand Intensive Society Adult Patient Database for 2016. Hospital mortality was modelled using logistic, probit and linear probability (LPM) models with intensive care (ICU) providers as fixed (FE) and random (RE) effects. Model comparison entailed indices of discrimination and calibration, information criteria (AIC and BIC) and binned residual analysis. Suspect covariate and ventilation treatment assignment endogeneity was identified by correlation between predictor variable and hospital mortality error terms, using the Stata™ “eprobit” estimator. Marginal effects were used to demonstrate effect estimate differences between probit and “eprobit” models. Results The cohort comprised 92,693 patients from 124 intensive care units (ICU) in calendar year 2016. Patients mean age was 61.8 (SD 17.5) years, 41.6% were female and APACHE III severity of illness score 54.5(25.6); 43.7% were ventilated. Of the models considered in predicting hospital mortality, logistic regression (with or without ICU FE) and RE logistic regression dominated, more so the latter using information criteria indices. The LPM suffered from many predictions outside the unit [0,1] interval and both poor discrimination and calibration. Error terms of hospital length of stay, an independent risk of death score and ventilation status were correlated with the mortality error term. Marked differences in the ventilation mortality marginal effect was demonstrated between the probit and the "eprobit" models which were scenario dependent. Endogeneity was not demonstrated for the APACHE III score. Conclusions Logistic regression accounting for provider effects was the preferred estimator for hospital mortality modelling. Endogeneity of covariates and treatment variables may be identified using appropriate modelling, but failure to do so yields problematic effect estimates.

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“…One must account for heteroskedasticity since it could result in misleading conclusions about coefficients and marginal effects interpretation (Greene 2012). Two approaches are used to calculate the marginal effects after probit models in applied works: (i) integrating with respect to individual effects, or (ii) assuming the individual effects to be null (Bland and Cook 2018). In the case (i), the probability of positive outcome is given by Pr(y it =…”

Section: Introductionmentioning

confidence: 99%

Heteroskedasticity in One-Way Error Component Probit Models

Moussa

2019

Econometrics

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This paper introduces an estimation procedure for a random effects probit model in presence of heteroskedasticity and a likelihood ratio test for homoskedasticity. The cases where the heteroskedasticity is due to individual effects or idiosyncratic errors or both are analyzed. Monte Carlo simulations show that the test performs well in the case of high degree of heteroskedasticity. Furthermore, the power of the test increases with larger individual and time dimensions. The robustness analysis shows that applying the wrong approach may generate misleading results except for the case where both individual effects and idiosyncratic errors are modelled as heteroskedastic.

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Random effects probit and logit: understanding predictions and marginal effects

Cited by 31 publications

References 6 publications

Clinic and care: associations with adolescent antiretroviral therapy adherence in a prospective cohort in South Africa

Clinic and care: associations with adolescent antiretroviral therapy adherence in a prospective cohort in South Africa

Modelling hospital outcome: problems with endogeneity

Heteroskedasticity in One-Way Error Component Probit Models

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