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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Is it possible to correct for bias in the tetrachoric correlations of rare events in small samples?

Background and Problem I am developing a meta-analytic epidemiological model to predict the prevalence of a series of related psychiatric disorders. As part of the modelling process, I need to ...
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two wave panel probit with random effect = bi-variate probit

According to the paper "Estimating Dynamic Models of Quit Behavior" [Journal of Labor Economics], it said "Bivariate probit is equivalent to probit random effects if there are only two waves in a ...
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Link between marginal effects of probit estimation and proportions in sample

Suppose you are estimating a model with a binary dependent variable $Y_i$ and where the explanatory variables are a randomly assigned binary treatment $D_i$ and a vector of covariates. My ...
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29 views

How to show probability satisfies probit model

This is an old past paper question that I am struggling to understand, so any help or hints would be appreciated... Consider the choice between two options, such as two product brands. Let $U_0$ ...
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Probit model rate of change

Consider a generalized linear model with a binary response variable Y and a predictor variable X and a probit link function. So the probability of success, $\pi(x)$, has the form ...
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65 views

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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12 views

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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8 views

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 - ...
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66 views

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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41 views

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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1answer
107 views

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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18 views

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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1answer
36 views

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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19 views

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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22 views

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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Instrumental variable standard errors smaller than naive estimator standard errors

I recently estimated the following model using 2 different estimators, multinomial probit and instrumental variable (IV) multinomial probit: $Product_{i}=\beta_0 + ...
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1answer
43 views

A very basic probit model doubt

So, I have just started going through binary choice models, and while explaining probit models- they start with how by specifying alternate distributions of the error term- we can use different ...
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1answer
24 views

Binary random variable, big data frame: does my approach make sense?

I have a large data frame with about 1100 columns containing integers and about 30'000 rows. The last column contains a binary random variable which attains values 0 and 1. 30% of the data frame ...
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1answer
31 views

Is it correct to use sampling weights for reducing multicollinearity in Probit?

I tried to estimate a probit model: $$y=b_1x_1+b_2x_2+b_3x_3,$$ where all variables are string and $x_1$ and $x_2$ are correlated. $x_1$ means GINI index and $x_2 = \text{self-employment rate}\cdot ...
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21 views

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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48 views

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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22 views

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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1answer
34 views

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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23 views

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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1answer
28 views

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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34 views

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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46 views

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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1answer
117 views

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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1answer
289 views

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 ...
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1answer
94 views

Computing elasticity of log-transformed variable in probit model

I would like to estimate the own-and cross-price elasticities of demand of a health product. Consider following model: ...
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21 views

Signing the inconsistency of a control functions estimator with an incomplete set of instruments

I've got a model of the form $$ y = 1\left(\alpha+\delta x+\beta_1\tilde v+\tilde\epsilon>0\right) $$ $x$ is endogenous, and $\tilde v$ is a control function residual: $$ \tilde v = ...
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24 views

Interaction vs. moderation, main effects

I am new to this forum and I hope that my questions have not been answered in other posts. I am still confused about moderation and interaction as some sources tell me that they are the same, others ...
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86 views

Beta coefficients of marginal effects

I am writing my master thesis and one of the main regression I perform is a probit. In order to compare the effect of different variables I want to show the different beta coefficients, but not of the ...
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21 views

Probit via MCMC with rare events

I like to estimate a mixed model via MCMC. I had to rely on MCMC, because there are some features in the model like spatial dependence that are much better to estimate with help of MCMC. My model is a ...
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78 views

How to estimate Heckprobit when there is a continuous endogenous regressor?

My model is following Y1=f(Y2 X1); Y1 is a binary variable and whether Y1 observed is depend on X1, X2. Meanwhile, Y2 is endogenous explanatory variabel which determined by Y2=f(X1 X3). My approach ...
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How do I prove that the the constant in the Probit model minimises its error of prediction?

Lets say the probit model Pr (Y=1|X) = F(xb). Where F is Fi and b is beta. How do I show that b = arg min E(y − Φ (xd))2
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Using Probit for Prediction - What to do about variance in the estimates?

Suppose I am estimating the following model: $Pr(Y=1|X) = \Phi(X'\beta + \epsilon)$ where $X = [X_1,X_2]$. Further suppose I end up with estimates for $X_1$ and $X_2$ of $\beta_1 = \beta_2 = ...
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In the linear probability model (probit or logit), should $\sum_i \hat p_i = 1$?

In the linear probability model (probit or logit), should $\sum_i \hat p_i = 1$?
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1answer
191 views

Predicted probabilities for probit model in R - categorical variable

I am running a probit regression with a random effect: m1<-glmer(Binary~Explan+(1|Random),family=binomial(link="probit")) where Explan is a three-level ...
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1answer
76 views

Interpreting interaction effects in probit regression model

I have run a probit regression model with one 2-way interaction and am having trouble interpreting the results. Both variables are categorical and so one level of ...
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1answer
88 views

Interpreting Marginal Effects

I am running a probit glmer, with a binary response varaible and a categorical explanatory variable with three dummy levels and have tried to calculate the marginal effect using the following code: ...
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28 views

Same result for post-hoc test and probit regression

I am getting the exact same results for a probit regression and post-hoc tests (simultaneous tests for linear hypotheses) - is this because I have used a dummy variable in the probit model and so it ...