# Binomial Logistic Regression

## Overview

The way you run Logistic Regressions in Jamovi is very similar to how you run Linear Regressions.  You should be familiar with most of the boxes and ways of running things. Hence, here we will not rehash everything.

In this tutorial, there will be step-by-step videos for Binomial, Multinominal and Ordinal regressions. Just like with linear regression you can also use block-wise-entry and generate plots and tables to visualise your results.

## Variables and Dataset

Skoczylis, Joshua, 2021, "Extremism, Life Experiences and the Internet", https://doi.org/10.7910/DVN/ICTI8T, Harvard Dataverse, Version 3.

### Binomial Logistic Regression

Dependent Variable:

For this analysis we have transformed the Extremism Score Scaled into a Binomial variable (the 75th percentile and above was coded as extreme, all others were coded as not extreme).

Independent Variables:

Social Media Use, Gender, Age, Confidence in Self, Racism Scale, Strain v Resilience Scale, and the interaction between Age*Social Media use.

### Ordinal/Multinominal Logistic Regression

Dependent Variable:

For this analysis we have transformed the Extremism Score Scaled into a ordinal variable (those with an extremism score of 0 have been classified as 'Not' Extreme', those with a score of between 0.1 and 2.75 have been classified as 'Extreme' and those with scores above 2.75 as 'Very Extreme').

Independent Variables:

Social Media Use, Gender, Age, confidence in self, Racism Scale, Strain v Resilience Scale, and Military Service.

Note: Using an Ordinal Regression will keep the order of the category in tact. In a Multinominal Regression, the order is lost.

## Logistic Regressions:  Step-by-Step Video Guide

You will find that running all of the Logistic Regressions is very similar to Linear Regressions. The main difference is, of course, the dependent variables you select. The other big difference, is that there are few assumptions.

The outputs are also interpreted slightly differently, as you will include the Odds Ratio. Below are three video guides that will take you through it step-by-step.

The first video is for a Binomial Regression

The next video introduces you to Multinominal Regressions

The final video will take you through Ordinal Regressions in Jamovi.

## Results: Logistic Regressions

1.

Here you will select your reference levels. This is important as you will be comparing the odds of something occurring or not.

Under Reference Levels select your chosen reference levels. In this case we have selected not Extreme and Male. 2.

Model Fit & Model Coefficients

In the Fit Measures add Overall Model - this will give you a p-value for your model.

In the Pseudo RSquared select McFaddens RSquared - this is the preferred option, but you can also select any or all of the other two too. If you do, note that the results may be slightly different, but they all give you the same a p-value for your model. For Logistic Regressions you also want to report the Odds Ratio.  Select this alongside the Confidence Intervals.

You can also add confidence intervals to your Estimate (the Log of the Odds Ratio). 3.

Binomial Logistic Regression: Results

McFadden's RSquared at 0.126 suggest that our model is a decent fit. The p-value also confirms that this model is statistically significant.

Looking at the our Model Coefficients we can see that Social Media Use is not a statistically significant predictor variable, but the interaction between Age and Social Media use is. That said this interaction only slightly increases the probability of being Extreme by 1.007 (CI 1.001 to 1.014).

The coefficients for gender suggest that women for example are 0.344 time more likely to be extreme than Men.

The coefficients for the Strain and Resilience variable indicates that for each increase in the score, you are 0.837 time more likely to be extreme. This suggest that the higher your strain is the more likely you are to be extreme. The plot below shows the interaction between Racism, Strain v Resilience and Age. The plot indicates that younger participants who have a higher than usual racism score and are experiencing higher strain are also more likely to also have more extremist attitudes. As someone becomes older this probability goes down 4.

Multinominal Logistic Regression: Results.

Here the extremism variable was split up into three categories 'Not Extreme', 'Extreme' and 'Very Extreme'. We can see that our model is statistically significant, but the McFadden RSquare indicates that the fit is not that great at 0.118.

Again, the coefficients suggest that women are 0.410 time (CI 0.32 and 0.527) more likely than men to me extreme v not extreme.

The strain v resilience variable suggest that each increase in the strain variable increases your likelihood of being 'very extreme' v 'not extreme' by 0.736 (CI 0.608 to 0.891).  However, strain is not significant in predicting a move from 'extreme' to 'not extreme' (p 0.130). Note: There are no plots available for Multinominal Logistic Regression

5.

Ordinal Logistic Regression: Results.

You interpret the output the same way you would a Binomial or Multinominal Logistic Regression.  For Ordinal Regressions you would also report the Thresholds - these are essentially the intercept of each category. The Threshold allows you to work which category your values fall into. Let's look at the example below:

If wanted to figure out what category a 45 year old Female falls into we would collect all the scores for each significant predictor variable and go through the following calculation

(Independent Variable 1*Model Coefficient)+(Independent Variable 2*Model Coefficient) + continue for each significant independent variable. You can get the outcome for some, or all of the significant predictor variables.

You then compare calculated value to the Model threshold. This should give you an indication of where your prediction would fall.

In practice it would look like this (the calculations is based on all of the predictor variables listed below):

(3*-0.472)+(0.5*-0.123)+(-1.5*-0.142)+(45*-0.028)+(0*-1.031)+(0*0.645) = -0.0335

Now let's look at which threshold this number is near. The threshold is between -1.602 ('Not Extreme') and 0.795 (Very Extreme').

We can therefore conclude that a person with the above characteristics would fall into the Extreme category.

To sum up: Get your details, workout through the above calculation, see which threshold your data would fall into.

Note: Jamovi does not provide plots for an ordinal regression.