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Estimation of Multivariate Probit Models via Bivariate Probit.

ABSTRACT: This paper suggests the utility of estimating multivariate probit (MVP) models using a chain of bivariate probit estimators. The proposed approach is based on Stata's biprobit and suest procedures and is driven by a Mata function. Two potential advantages over Stata's mvprobit procedure are suggested: significant reductions in computation time; and essentially unlimited dimensionality of the outcome set. The time savings arise because the proposed approach does not rely simulation methods; the dimension advantage arises because only pairs of outcomes are considered at each estimation stage. Importantly, the proposed approach provides a consistent estimator of all the MVP model's parameters under the same assumptions required for consistent estimation via mvprobit, and simulation exercises reported below suggest no loss of estimator precision relative to mvprobit.

SUBMITTER: Mullahy J

PROVIDER: S-EPMC6957230 | biostudies-literature | 2016 Mar

REPOSITORIES: biostudies-literature

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Estimation of Multivariate Probit Models via Bivariate Probit.

Mullahy John J

The Stata journal 20160301 1

This paper suggests the utility of estimating multivariate probit (MVP) models using a chain of bivariate probit estimators. The proposed approach is based on Stata's biprobit and suest procedures and is driven by a Mata function. Two potential advantages over Stata's mvprobit procedure are suggested: significant reductions in computation time; and essentially unlimited dimensionality of the outcome set. The time savings arise because the proposed approach does not rely simu ...[more]

PMID: 31933544

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Project description:BACKGROUND: When multiple endpoints are of interest in evidence synthesis, a multivariate meta-analysis can jointly synthesise those endpoints and utilise their correlation. A multivariate random-effects meta-analysis must incorporate and estimate the between-study correlation (rhoB). METHODS: In this paper we assess maximum likelihood estimation of a general normal model and a generalised model for bivariate random-effects meta-analysis (BRMA). We consider two applied examples, one involving a diagnostic marker and the other a surrogate outcome. These motivate a simulation study where estimation properties from BRMA are compared with those from two separate univariate random-effects meta-analyses (URMAs), the traditional approach. RESULTS: The normal BRMA model estimates rhoB as -1 in both applied examples. Analytically we show this is due to the maximum likelihood estimator sensibly truncating the between-study covariance matrix on the boundary of its parameter space. Our simulations reveal this commonly occurs when the number of studies is small or the within-study variation is relatively large; it also causes upwardly biased between-study variance estimates, which are inflated to compensate for the restriction on rhoB. Importantly, this does not induce any systematic bias in the pooled estimates and produces conservative standard errors and mean-square errors. Furthermore, the normal BRMA is preferable to two normal URMAs; the mean-square error and standard error of pooled estimates is generally smaller in the BRMA, especially given data missing at random. For meta-analysis of proportions we then show that a generalised BRMA model is better still. This correctly uses a binomial rather than normal distribution, and produces better estimates than the normal BRMA and also two generalised URMAs; however the model may sometimes not converge due to difficulties estimating rhoB. CONCLUSION: A BRMA model offers numerous advantages over separate univariate synthesises; this paper highlights some of these benefits in both a normal and generalised modelling framework, and examines the estimation of between-study correlation to aid practitioners.

Dataset Information

Estimation of Multivariate Probit Models via Bivariate Probit.

Publications

Estimation of Multivariate Probit Models via Bivariate Probit.

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