bivariate probit model

Copyright © 2014 Francesca Ieva et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this work we analyse the relationship among in-hospital mortality and a treatment effectiveness outcome in patients affected by ST-Elevation myocardial infarction. The main idea is to carry out a joint modeling of the two outcomes applying a Semiparametric Bivariate Probit Model to data arising from a clinical registry called STEMI Archive. A realistic quantification of the relationship between outcomes can be problematic for several reasons. First, latent factors associated with hospitals organization can affect the treatment efficacy and/or interact with patient’s condition at admission time. Moreover, they can also directly influence the mortality outcome. Such factors can be hardly measurable. Thus, the use of classical estimation methods will clearly result in inconsistent or biased parameter estimates. Secondly, covariate-outcomes relationships can exhibit nonlinear patterns. Provided that proper statistical methods for model fitting in such framework are available, it is possible to employ a simultaneous estimation approach to account for unobservable confounders. Such a framework can also provide flexible covariate structures and model the whole conditional distribution of the response.

Instrumental variable techniques are widely used for isolating the effect of a given predictor in the presence of unobserved confounding (e.g. Wooldridge 2010; Marra & Radice 2011b and references therein), and are increasingly used in epidemiological and medical studies (e.g. Goldman et al . 2001 and references therein). In the context of binary responses, it is well known, from both theoretical and empirical results, that bivariate like- lihood estimation methods are superior to conventional two-stage instrumental variable procedures (e.g. Bhattacharya et al . 2006; Wooldridge 2010). First introduced by Heck- man (1978), the recursive bivariate probit model represents an effective way to estimate the effect a binary regressor has on a binary outcome in the presence of unobservables. The semiparametric version of Heckman ’ s model is an important extension since unde- tected nonlinearity can have severe consequences on the estimation of covariate effects (e.g. Marra & Radice 2011a). Chib & Greenberg (2007) proposed two Bayesian fi tting procedures for the class of instrumental variable models including the semiparametric recursive bivariate probit model. However, as the authors point out, very large sample sizes are required to obtain reasonable estimates of the binary treatment effect, hence undermining the utility of the method for practical modeling. Marra & Radice (2011a) considered the same model and introduced a penalized likelihood based procedure which permits reliable estimation of the model coef fi cients at reasonably small sample sizes.

Instrumental variable techniques are widely used for isolating the effect of a given predictor in the presence of unobserved confounding (e.g. Wooldridge 2010; Marra & Radice 2011b and references therein), and are increasingly used in epidemiological and medical studies (e.g. Goldman et al . 2001 and references therein). In the context of binary responses, it is well known, from both theoretical and empirical results, that bivariate like- lihood estimation methods are superior to conventional two-stage instrumental variable procedures (e.g. Bhattacharya et al . 2006; Wooldridge 2010). First introduced by Heck- man (1978), the recursive bivariate probit model represents an effective way to estimate the effect a binary regressor has on a binary outcome in the presence of unobservables. The semiparametric version of Heckman ’ s model is an important extension since unde- tected nonlinearity can have severe consequences on the estimation of covariate effects (e.g. Marra & Radice 2011a). Chib & Greenberg (2007) proposed two Bayesian fi tting procedures for the class of instrumental variable models including the semiparametric recursive bivariate probit model. However, as the authors point out, very large sample sizes are required to obtain reasonable estimates of the binary treatment effect, hence undermining the utility of the method for practical modeling. Marra & Radice (2011a) considered the same model and introduced a penalized likelihood based procedure which permits reliable estimation of the model coef fi cients at reasonably small sample sizes.

Copyright © 2014 Francesca Ieva et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this work we analyse the relationship among in-hospital mortality and a treatment effectiveness outcome in patients affected by ST-Elevation myocardial infarction. The main idea is to carry out a joint modeling of the two outcomes applying a Semiparametric Bivariate Probit Model to data arising from a clinical registry called STEMI Archive. A realistic quantification of the relationship between outcomes can be problematic for several reasons. First, latent factors associated with hospitals organization can affect the treatment efficacy and/or interact with patient’s condition at admission time. Moreover, they can also directly influence the mortality outcome. Such factors can be hardly measurable. Thus, the use of classical estimation methods will clearly result in inconsistent or biased parameter estimates. Secondly, covariate-outcomes relationships can exhibit nonlinear patterns. Provided that proper statistical methods for model fitting in such framework are available, it is possible to employ a simultaneous estimation approach to account for unobservable confounders. Such a framework can also provide flexible covariate structures and model the whole conditional distribution of the response.

To understand causes for auditor switching, we also employ the five control variables in the switching model according to prior studies (Krishnan, 1994; Menon and Schwartz, 1985). However, client size inhibits auditor switching (Haskins and Williams, 1990; Krishnan, 1994) since smaller firms grow rapidly in general and tend to switch to bigger CPA firms unlike larger firms, who are deterred by higher switching costs. Sample selection bias occurs when the sample is not selected randomly but only from clients issued with IGCQ. To overcome the bias, we apply the bivariate probit method, which can reveal unobservable factors affecting delisting and auditor switching. The research model is designed as follows:

In 2002, the German government tried to increase private old-age provisions by introducing incentives such as supplementary subsidies and tax credits. Since then, the so- called “Riester pension” has grown in popularity. Apart from subsidized pension plans, unsubsidized private pension insurances as an instrument for old-age have been enormously important for a long time. With data for the years 2005 to 2009 from the German SAVE study, we analyze whether the decision for a “Riester pension” is independent of the decision for unsubsidized private pension insurance using methods for simultaneous equations. Our estimation results indicate that decisions on “Riester” and private pensions are not independent and the proposed random-parameters bivariate probit model results in efficiency gains compared to single probit estimations. Regarding governmental subsidies, we find positive incentive effects of child subsidies whereas low income earners are not induced to increase their old-age provisions. Further, there is strong evidence for a “crowding - in” among alternative assets as well as a significant effect of demand inducement. Finally, considering the saving motives, individuals do not take a “Riester pension” because of securing pension payments only but

To estimate this model, we would have to make two assumptions that could yield inconsistent and biased estimates. First, we would have to assume that all the differences between recipient and non-recipient households are explained by the characteristics in γ . However, remittances are a consequence of migration, and if migration has an effect on education in addition to its effect through remittances, the error term in (9) would suffer from omitted variable bias (Mckenzie 2006). Second, we would have to assume that the child schooling decisions are not correlated with the decision of a migrant to send back remittances. In fact, if schooling, migration, and remittance decisions are correlated, then we would run into a simultaneous causality problem. To address this potential endogene- ity, we use a bivariate probit model to account for the presence of r as a binary endogenous variable (Roodman 2011) that equals one if the household receives remittances and zero otherwise. In Section 6.3, we verify our results by repeating the analysis on households without migration and reach a similar conclusion. The empirical counterpart of Eq. (7) is given by the following recursive model:

The Bivariate probit model use binary dependent variable, where two equations are estimated. It represents decisions that are interrelated rather than independent. In these models the assumption is that the errors are drawn from a standard bivariate normal distribution with zero means (Li, Poskitt & Zhao, 2016). In this case, the null hypothesis is that there is no significant difference between the characteristics of the farmers and the adoption of any of two agricultural technologies. In order to test the null hypothesis, one can either estimate two separate probit models or a bivariate probit. But, since the correlation coefficient (rho) is statistically significant, two separate probit models would generate biased estimates, that is, the decisions to use mechanization and improved seeds are interrelated, so the bivariate probit model was used.

This paper analyses the extent to which existing econometric models of low-pay transition probabilities in Italy are biased by the presence of endogenous panel attrition. Non-random exits from the sample of wage earners may result from both demand and supply side factors and this could lead to under- or overestimation (respectively) of the extent of low-wage persistence. The analysis is carried out by extending the bivariate probit model used in Cappellari [1999] (where starting state and transition probabilities are jointly modelled thus tackling the endogeneity of the conditioning starting wage state) with a third equation which controls for the non-randomness of panel attrition. The resulting trivariate probit model with endogenous switching, whose evaluation is not feasible within the routines customarily available in microeconometric packages, is implemented by applying simulation estimation techniques. Results show the ignorability of attrition in SHIW data, thus pointing towards the robustness of the results previously obtained without controlling for attrition.

In this paper, we discuss on the problem of testing Granger causality with a bivariate dynamic probit model taking into account the initial conditions. The organization of this paper is the following one. In Section 2 we explain the causality test method for bivariate probit model with panel data. In Section 3, we describe the estimation method available when the likelihood function has an intractable form (two dimensions integral in our case). Section 4 presents the calculation of the gradient with respect to the model parameters and the calculation of the Hessian matrix with respect to the random effects vector. In Section 5, we present a robustness analysis of our selected estimation method by doing some simulations 1 .

To identify bank misconduct, we employ a unique dataset of regulatory enforcement actions issued by the three US supervisory bodies (the Federal Reserve Board (FRB), the Federal Deposit Insurance Corporation (FDIC) and the Office of the Comptroller of the Currency (OCC)) against banks that engage in unsafe, unsound and illegal banking practices which violate laws. One concern with our analysis is that we can only observe detected misconduct (once an enforcement action has been issued), but not the population of all committed cases of misconduct. That is, even in the absence of enforcement actions, a bank may still have engaged in undetected misconduct. To address this problem of partial observability, we follow Wang (2013) and Wang et al. (2010) to employ a bivariate probit model that disentangles committing misconduct from the detection of misconduct conditional upon misconduct having occurred.

Indeed, the likelihood ratio test retains the smallest distance between empirical and nominal size at the nodes presented by the small multiple. Sorting through its rows makes the distance as well as the size advantage over other procedures decline at a diminishing rate with sample information available. This monotonicity is stalled in case of DGP2 and DGP3. Here graphical observation detects a marked pattern of under-rejection for small samples in the vicinity of conventional significance levels. If information is sufficient LR is also the only procedure to remain within 0.05 critical values of the Kolmogorov-Smirnov test, delimiting the shaded area: for DGP1 and 1,000 or 2,000 observations the null, differences of the P value plot from the P values’ theoretical cumulative distribution are due entirely to experimental randomness, can no longer be rejected at the 5 per cent significance level. Furthermore, having to evaluate the bivariate probit model from non-standard samples does not always

This paper’s goal is to identify the sources of expenditure and poverty dynamics among Malawian households between 1998 and 2002 and to model poverty transitions in Malawi using a bivariate probit model with endogenous selection to address the "initial conditions' problem. The exogeneity of the initial state is strongly rejected and could result in considerable overstatement of the effects of the explanatory factors. The results of the bivariate probit model do indicate that education of the household head, per capita acreage cultivated and changes in household size are significantly related to the probability of being poor in 2002 irrespective of the poverty status in 1998. For those households who were poor in 1998, the probability of being poor in 2002 was significantly influenced by household size, value of livestock owned and mean time to services, while residence in the Northern region was a significant variable in determining the probability of being poor in 2002 for households that were not poor in 1998.

Using the bivariate probit model, the coefficient for males decreases somewhat but remains negative while for females it now is very close to zero. However, standard errors increase in both models and the results turn insignificant (see Table III). The likelihood-ratio test does not reject the null hypothesis of no correlation between the disturbance terms of equations 2 and 3 for males and females, suggesting exogeneity of diabetes. The test for normality of the error term does not reject normality for the male and the female model, increasing our confidence in the estimates. Nonetheless we consider the results of the linear IV model: the test statistics indicate sufficiently strong and valid instruments, as shown by the F statistic and Hansen J statistic for overidentification, respectively. The coefficients of the linear IV model are very different from the bivariate probit model, turning positive for males and females, but also very imprecise as indicated by the large standard errors (see Table IV). As mentioned before, Chiburis et al. (2012) show that the estimates of the linear IV model are likely to be imprecise when low treatment probabilities exist and can differ substantially from the bivariate probit model, which seems to be the case here. 8

Access to credit remains a mirage to a majority in Kenya. Only 39.6% of Kenya’s adult population has access to credit products in Kenya (FSD, 2009). Viewed against a backdrop of growing evidence of rising cost of living, low or no access to credit inhibits both consumption and investment smoothing thus accelerating poverty levels. A bivariate probit model, applied on Fin Access 2009 national survey data revealed that social capital enhances financial inclusion through increased access to informal loans. The study recommends that financial institutions should factor in group affiliation in designing their loan products so as to increase financial outreach.

A likelihood ratio test of the significance of is a direct test of the endogeneity of malaria prevalence and ITN use (Wooldridge, 2002 cited in Morris, 2004). If , then it is appropriate to use probit or logit model. If is non-zero ( then ITN use and malaria prevalence are endogenous. This means that the probit or logit results are biased giving the need for preferring the recursive bivariate probit model to either probit or logit model. Controlling for endogeneity in a bivariate probit framework requires suitable instruments (in this case, source of ITN ownership) for ITN usage. The instruments should have the property of non-weakness, which means that source of ITN ownership should be strongly correlated with ITN use but uncorrelated with the error term in the malaria prevalence equation given that the other independent variables have been netted out (α ≠ 0| ). If this condition does not hold, then recursive bivariate probit model estimators will be inconsistent because the instrument itself is endogenous (Wooldridge, 2002; Cameron & Trivedi, 2005). A justification that these conditions have been satisfied is presented in appendix A. In appendix B, we present the definition, measurement and the a’prori expected signs of all the variables included in the study.

This paper is concerned with the Bayesian estimation of a Multivariate Probit model. In particular, this paper provides an algorithm that obtains draws with low correlation much faster than a pure Gibbs sampling algorithm. The algorithm consists in sampling some characteristics of slope and variance parameters marginally on the latent data. Estimations with simulated datasets illustrate that the proposed algorithm can be much faster than a pure Gibbs sampling algorithm. For some datasets, the algorithm is also much faster than the efficient algorithm proposed by Liu and Wu (1999) in the context of the univariate Probit model.

On a quarterly frequency, we explore the ability of macroeconomic and financial variables to report to analysts the probability of GDP being in a boom environment. The macroeconomic variables are the industrial production, the import prices, the consumer price index, the money supply, and the economic sentiment indicator. The financial variables are the Athens stock exchange index and its realized volatility, the Baltic Dry Cargo Index, and the 10-year government bond spread. A probit regression model transforms the economic and financial variables into information that expresses the probability of the economy not being in recession; in other words the probability of q-o-q GDP being positive.

The rest of this paper is organized as follows: in Section 2, we present a conventional formulation of topic modeling along with our general notation and the correlated topic models extension. Section 3 introduces our adaptation of the diagonal orthant probit model to topic discovery in the presence correlations among topics, along with the corresponding auxiliary variable sampling scheme for updating the probit model parameters and the remainder of all the posterior distributions of the parameters of the model. Unlike with the logistic normal formulation where the non-conjugacy leads to the need for sophisticated sampling scheme, in this section we clearly reveal the simplicity of our proposed method resulting from the natural conjugacy inherent in the aux- iliary formulation of the updating of the parameters. We also show compelling computational demonstrations of the efficiency of the diagonal orthant approach compared to the traditional multinomial probit for on both the auxiliary variable sampling and the estimation of the topic distribution. Section 4 presents the performance of our proposed approach on the Associated Press data set, featuring the intuitively appealing topics discovered, along with the correlation structure among topics and the loglikelihood as a function of topical space dimension. Section 5 deals with our conclusion, discussion and elements of our future work.

Aphid abundance and species richness were not zero-inflated and were assessed using a general- ized mixed-effects model, with a Poisson distribu- tion. Because some sites were sampled in more than one year, sampling site was included as a ran- dom effect. Similarly, because the WI results were not zero-inflated, all response variables were ana- lyzed using generalized mixed-effects linear regression model with a Poisson distribution. Because sites were not sampled in both years, the sampling site was not included as a random effect. The average percent cropland and unmanaged land and the average number of aphids per trap of the two study regions were compared using Wilcoxon signed-rank tests. All analyses were conducted in STATA (StataCorp, College Station, Texas, USA) (SE-64, version 15) and R (version 3.2.1).