# Tagged Questions

This refers generally to statistical procedures that utilize the probit function. The primary example of which is probit regression where the probit transformation of the parameter p of a binary response distribution is used as a link.

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### Endogenous ordered probit (Stata, R)

main equation $y_1 = y_2 \beta + x_1 \gamma + u_i$ Instrumental equation $y_2=x_1 \pi_1 + x_2 \pi_2$ I have a binary endogenous variable $y_2$ in my main estimation equation. My instrument $x_2$...
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### 2SLS - 2 OLS for 2 endogenous variables in 1st stage and logit/probit in the 2nd stage?

I came across this question (here) saying that I can manually run an OLS in the 1st stage with the endogenous variable as dependent variable (i.e. the instrument) get the fitted values for the ...
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### Probit with more than one instrument

I am estimating a probit model with instruments in R (using ivprobit). My simplified model looks like this: ...
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### Ordered Probit Regression Results Interpretation

Suppose I have an opinion survey on some topic. Both my dependent variable and independent variable are categorical variables. My question is, if I use the ordered probit model, how do I interpret the ...
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### Compare p-value/z-statistic from probit reporting marginal effects with a standard probit without marginal effects

I have results from different empirical studies. Some of them report results for probit/logit models, others report the marginal effects. I want to compare the statistical significance between the ...
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### Derive z- or t-statistic from p-values of regression coefficients from a probit/logit model

I have the results from an empirical study reporting the results for a probit and logit model. They just report the p-values of the regression coefficients. I want to derive the corresponding $t$-/$z$-...
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### prediction of Random Effect (BLUP) in unique model framework

Basic question: Is there any method that could predict the random effect in different model framework than GLMM(generalized linear mixed model)? while I was reading ...
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### Is there any other way to get LD50 for these cases when Probit does not yield results?

To determine a lethal dose 50 (LD50) (ie the dose or concentration of a compound that kills 50% of the insects) I have done a Probit regression. In some cases, the p square CHI is > 0.05 or the ...
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### Elasticity vs marginal effects in probit models with logarithmic and dummy independent variables

I am trying to estimate a model with probit in stata of this form: p(y=1|x)=a+bi(ln(xi))+bj(xj)+e where xj are dummy variables and ln(xi) are continuos variables in logarithms. How do i interpret ...
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### Model comparison using lower bound from variational approximation

I applied variational approximation for probit regression model and got the lower bound for the log marginal likelihood. When I compare models with different covariates using lower bound, I found that ...
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### How to find gamma coefficients?

I am trying to replicate this paper "Gleditsch, Kristian Skrede and Michael D. Ward. 2006. "Diffusion and the International Context of Democratization", International Organization 50: 911-933" and I ...
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### Pratio and the Probit Model

The question is: The below displays results for a probit model where the dependent variable, Y, equals 1 if Coke was chosen by individual i and 0 if Pepsi was chosen by individual i. Y = 1.4727 - 1....
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### How to choose between logit, probit or linear probability model?

To decide whether to use logit, probit or a linear probability model I compared the marginal effects of the logit/probit models to the coefficients of the variables in the linear probability model. ...
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### Tie out probit models from polr and mlogit

I'd like to run a probit regression on the "B1_df" data frame with 3 categorical outcome variables (rank 1,2 or 3). I cannot use glm because there are 3 outcome variables. I would like to be able to ...
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### Is it meaningful to compare a logit and probit model with the same no. of observations and independent variables using AIC and BIC?

For my dissertation i want to show that the logit and probit model produce the same results. So far i've compared the marginal effects, percent correctly predicted and done a scatter plot of the ...
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### Probit/Logit Model - How to find the parameter $\beta$

I am confused on how to calculate the beta in a probit/logit model Probit Model $P(Y_i=1)=\Phi(X'\beta)$ Logit Model: $P(Y_i=1)=e^{X'\beta}/(1+e^{X'\beta})$ These formula's are great but how do I ...
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### Explanation for negative cross-price elasticities if the two alternatives cannot be complements

I would like some help in interpreting some odd cross-price elasticities that I got from my model. I estimated the following multinomial probit model and calculated the elasticities post-estimation: ...
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### Standard error for intercept only model in probit regression

How do you calculate the standard error for intercept for an intercept only probit regression model? I was expecting the formula to be: 1 / sqrt(N * p * (1 - p)) where N = no. of obs, p = mean(y). ...
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### conditional marginal effect at the mean is the same as the average of the conditional marginal effect in the Linear Probability model?

I know that MEM and AVE is rather different in a probit and logit model, but it is true that these two values are the same in the Linear Probability model ?
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### Are there any situations in which an OLS estimation of probability (with a binary dependent variable) might come in handy? [duplicate]

Most textbooks that I've read mention the nonsensical results that you might obtain with an OLS estimation of a probability of a variable being 0 or 1 -- as such, you use the transformations of the ...
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### OLS and Probit Model regarding a dummy variable being dropped

I've been trying to run a regression using a probit model, but I keep getting a dummy variable being dropped from the regression (in Stata's output) because it predicts the success perfectly. The OLS ...
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### How to estimate the parameters of the following log-likelihood function?

I would like to estimate the parameters based on the famous Merton model used probability of default modelling: Suppose firms' logarithmic returns are following the standard normal distribution and ...
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### Mean and Standard Error of True Percentages (Not Binomial Proportions)

In my line of work I occasionally deal with data on the percent lipid of fish fillet (environmental sampling). The question came up today about how to calculate the mean and standard error and ...
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### The likelihood of response variables in variational Bayesian probit regression

I read the paper Explaining Variational Approximations (J.T. Ormerod & M.P. Wand) and there is a part where they explain variational probit regression with auxiliary variable since the posterior ...
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### testing nonlinear hypothesis glm R

I estimate probit model: \begin{align*} P(y=1|x_1, x_2, x_3) = \Phi(\alpha_0 + \alpha_1 x_1 + \alpha_2 x_2+ \alpha_3 x_3) \end{align*} using: ...
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### Tests for mprobit

I have a multinomial probit model with explicative variables that are also all either categorical or binary. I would like to know which are the main statistical tests that I should do before analysing ...
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### Probit Model: Interpretation of marginal effects if explanatory variables are proportions

How do I interpret the marginal effect of an explanatory variable that is a proportion in a probit model? For example if I get a marginal effect of 0.8 does this mean that if the proportion increases ...
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### Definition of ordered probit

Can someone please provide a definition of the ordered probit model so that I can calculate the value of $\Pr(y \le k | \mathbf{x})$, i.e. probability of observation falling in the $k$-th class or ...
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### Two-Part Model with Panel Regression

Can I estimate in the first part (using probit/logit) of the 2P-Model the probability of an event to occur (using an indicator variable where ind = 0 if dep=0 and ind = 1 if dep>0) and in the second ...
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### Probit/Logistic Regression: Predicted probabilities vs. marginal effects

I have a very basic question on post-estimation for probit/logistic regression models (frequentist). The non-linear character of the link functions requires us to do post-estimation for a sensible ...
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### Estimating unexplained variance from multivariate probit output (for imputation protocol)

I have a use case in which survey data underreports program participation, and I need to impute new recipients from within the survey data. There are two (exogenously provided) sub-objectives: ...
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### Is there a theoretical distribution for the residuals of a logit/probit regression?

I know there are a number of ways to define residuals for logit/probit regression but is there any theoretical distribution? I've also heard these residuals can be bimodal so maybe there is no closed ...
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### how to perform correlation analysis between binary and continuous variables?

Can any one tell me how to perform correlation analysis between binary and continuous variables? I have to do this analysis for publication wherein we are trying to construct between binary and ...
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### How can I calculate this integral? $\int_{-\infty}^{\infty} \Phi (a + bX) \phi (c + eX) dx$

Suppose we have the density and distribution of the standard normal. How can one calculate the integral: $\int_{-\infty}^{\infty} \Phi (a + bX) \phi (c + eX) dx$ Note this is not included in the ...
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### Using IV Probit in Stata

I am trying to estimate an IV model where my dependent variable is on the 0-1 scale, which is why I want a Probit estimator. However, my independent variable is a continuous, endogenous variable. For ...