## Linear vs. Logistic Probability Models: Which is Better, and When?

Interpretability Let’s start by comparing the two models explicitly. If the outcome Y is a dichotomy with values 1 and 0, define p = E(Y|X), which is just the probability that Y is 1, given some value of the regressors X. Then the linear and logistic probability models are: p = a0 + a1X1 + a2X2 + … + akXk (linear) ln[p/(1-p)] = b0 + b1X1 + b2X2 + … + bkXk (logistic) […]

## The Difference Between the Bernoulli and Binomial Distributions

You might already be familiar with the binomial distribution. It describes the scenario where the result of an observation is binary—it can be one of two outcomes. You might label the outcomes as “success” and “failure” (or not!). Or, if you want to get mathematical about it, you might label them “1” and “0.” You […]

## Logistic Regression Analysis: Understanding Odds and Probability

Probability and odds measure the same thing: the likelihood or propensity or possibility of a specific outcome. People use the terms odds and probability interchangeably in casual usage, but that is unfortunate. It just creates confusion because they are not equivalent. How Odds and Probability Differ They measure the same thing on different scales. Imagine how confusing it would be […]

## How to Conduct Probit and Logit Models (Binary Outcome Models)

Probit and Logit Models (Binary Outcome Models) Do you want to understand the factors that influence binary outcomes? Then you’ve come to the right place. In this article, we’ll delve into the world of Probit and Logit models, which are commonly used in statistical analysis to predict binary outcomes. Whether you’re a researcher, […]

## Logistic Regression Analysis: Understanding Odds and Probability

Probability and odds measure the same thing: the likelihood or propensity or possibility of a specific outcome. People use the terms odds and probability interchangeably in casual usage, but that is unfortunate. It just creates confusion because they are not equivalent. How Odds and Probability Differ They measure the same thing on different scales. Imagine how confusing it would be […]

## The Difference between Logistic and Probit Regression

Both are types of generalized linear models. This means they have this form: Both can be used for modeling the relationship between one or more numerical or categorical predictor variables and a categorical outcome. Both have versions for binary, ordinal, or multinomial categorical outcomes. And each of these requires specific coding of the outcome. For example, in both logistic and […]

## How to perform Panel data regression for random effect model in STATA

The previous article (Pooled panel data regression in STATA) showed how to conduct pooled regression analysis with dummies of 30 American companies. The results revealed that the joint hypothesis of dummies reject the null hypothesis that these companies do not have any alternative or joint effects. Therefore pooled regression is not a favourable technique for the panel […]

## What is panel data analysis in STATA

The previous articles in this module showed how to perform time series analysis on a dataset where observations are present for days, weeks, months, quarters or years. This article of the module explains how to perform panel data analysis using STATA. In the case of panel data, the observations are present in time and space dimensions. For […]

## ARCH model for time series analysis in STATA

The previous article showed how to initiate the AutoRegressive Conditional Heteroskedasticity (ARCH) model on a financial stock return time series for period 1990 to 2016. It showed results for stationarity, volatility, normality and autocorrelation on a differenced log of stock returns. The article concluded that the series has an ARCH effect. In continuation, this article presents the ARCH model of the same series. Applying […]

## How to identify ARCH effect for time series analysis in STATA

The previous articles showed how to apply Vector Auto Regression (VAR) and Vector Error Correction Model (VECM) based on the assumption that the variables either have a long run or short run causality among them. Some financial time series such as stock returns show wide swings for an extended period of time. Such behaviour is known as volatility. Volatility only represents […]