Refer to the death penalty data with a binary interpretation of the response for presence or absence of death penalty (see Exercises 10 and 13). Consider a model consisting of the variables LEGAL, HDI, and GNI. Assess the model fit and identify any concerns.

Exercises 13

Refer to the death penalty data given in Exercise 10. Identify which variables are related to the binary response "Allows Death Penalty" (STATUS is a, b, or c) versus "No Death Penalty" (STATUS is d). Form a model and use the model to estimate the probabilities that the United States and Canada would allow the death penalty.

Exercise 10

A criminologist studying capital punishment was interested in identifying whether certain social, economic, and political attributes of a country related to its use of the death penalty. She gathered data from public sources on 194 countries, recording the following variables:

• COUNTRY: The name of the country;

• STATUS: The country's laws on death penalties, coded as a = Public executions; b = Private executions; c = Executions allowed but none carried out in last 10 years; d = No death penalty;

• LEGAL: The basis for the country's legal system, coded as a = Islamic; b = Civil; c = Common; d = Civil/Common; e = Socialist; f = Other;

• HDI: Human Development Index, a numerical measure ranging from 0 (very low human development) to 1 (very high human development);

• GINI: GINI Index of income inequality, a numerical measure ranging from 0 (perfect equality) to 1 (perfect inequality);

• GNI: Gross National Income per capita (US$);

• LITERACY: Literacy rate (% of adults aged 15 and above who are literate);

• URBAN: Percentage of total population living in urban areas;

• POL: Political Instability Index for the level of threat posed to governments by social protest, a numerical measure ranging from 0 (no risk) to 10 (high risk);

• CONFLICT: Level of conflict experienced in the country, coded as a = No conflict, b = latent (non-violent) conflict, c = manifest conflict, d = crisis, e = severe crisis, f = war.

The data for the 141 countries with complete records are available in the DeathPenalty.csv file.11 The response variable is the country's death penalty status, while all other variables except COUNTRY are explanatory.

(a) Fit a multinomial (nominal response) regression model to these data using all available explanatory variables as linear terms. Compute the AIC and the BIC for this model. Also compute AICc by using the formula on page 267. Note that the model degrees of freedom that are needed for computing AICc can be found from the extractAIC() function.

(b) Explain why STATUS can be viewed as an ordinal variable.

(c) Fit a proportional odds regression model (see Section 3.4) to these data using all available explanatory variables. Compute AIC, BIC, and AICc as in the multinomial regression model.

(d) Note that the proportional odds model assumes both the ordinality of the response and equal coefficients across different logits. Based on the information criteria, is there evidence to suggest that these assumptions lead to a poor model fit? Explain.