## Multinomial logistic regression is the use of logistic regression when there are more than two levels of the categorical response variable.

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##### Description

Multinomial logistic regression is the use of logistic regression when there are more than two levels of the categorical response variable.

You will be using data about the United States to predict how extraverted people are from different parts of the country and the role of politics. The data includes region: North-East, West, etc; it includes generalized personality assessments of people and political party of the governor of each state.

With this lab we will predict Extraversion as an ordinal variable (variable name is ExtrOrd and a bigger number means people are more extraverted/outgoing) using the categorical variables "region" and "Governor" as Factors.

Start by making sure your data are the correct format (continuous, ordinal, nominal).

Create a Contingency table with region as rows and ExtraOrd as columns. Make sure to look at the Bar Plot.

Now build an Logistic Regression Model with Ordinal Outcomes. You are predicting ExtraOrd with region and Governor. Build your model in three blocks. 1) region, 2) Governor 3) The intraction between region and Governor. Pay attention to the AIC value and think back to what we learned in the lecture. Use the NorthEast and Republican as reference levels.

Now, it is also said that those folks in the North-East tend to be a bit more Neurotic than the rest of the country. The data actually confirms this statement if you run a one-way ANOVA on it! Therefore, include Neuroticism in the model as a fourth Block. Now interpret what you have!

Question 1: Based on the bar plot, which region is the most Extraverted?

Question 2: Based on the bar plot, which region is the least Extraverted?

Question 3: Which model has the best AIC value?

Question 4: In model 3 before Neuroticism is added to the model, there is a significant interaction term at alpha = 0.05. - T or F?

Question 5: In model 4, the main effect of Governor is significant at alpa = 0.05 - T or F?

Question 6: In model 4, Neuroticism and Extraversion are significantly related at alpha = 0.05 - T or F?

USING MODEL 4 ANSWER THE FOLLOWING QUESTIONS.

These questions are about the directionality of the estimates. What do positive and negative values mean?

To answer these question look at the parameters comparing the regions. What direction is the comparison of Midwest - Northeast? What direction is the comparison of West - Northeast? Figure out what the signs mean based on the bar plot from the Contingency table.

Question 7: Having a Democrat governor is related to people being more extraverted than having a Republican governor  - T or F?

Question 8: Having greater Neuroticism makes people more extraverted - T or F?

Question 9: Despite beneficial effects of having a Democratic governor, being in the West still less extraverted than being in the Northeast - T or F?