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Question 2. In a medical experiment, two different treatment methods are randoml...

Apr 11, 2024

Question 2. In a medical experiment, two different treatment methods are randomly assigned to diabetes patients. The results are as follows. The numbers in the table refer to the number of cases. \begin{tabular}{|l|l|lll|} \hline Treatment & Sex & Worsened & No change & Improved \\ \hline A & Male & 155 & 215 & 280 \\ & Female & 75 & 180 & 95 \\ \hline B & Male & 85 & 95 & 75 \\ & Female & 55 & 40 & 25 \\ \hline \end{tabular} (a) [10 marks] Fit a multinomial regression model with main effects for treatment and sex using R. Please provide R codes.

Solution by Steps

step 1

To fit a multinomial regression model in R, we first need to organize the data into a format suitable for analysis. We will create a data frame with the counts, treatment, sex, and outcome variables

step 2

Install and load the 'nnet' package in R, which contains the function 'multinom' for fitting multinomial logistic regression models. Use the following R code: ```

R install.packages("nnet") library(nnet)

R treatment <- rep(c("A", "B"), each = 6) sex <- rep(c("Male", "Female"), each = 3, times = 2) outcome <- rep(c("Worsened", "No change", "Improved"), times = 4) counts <- c(155, 215, 280, 75, 180, 95, 85, 95, 75, 55, 40, 25) data <- data.frame(treatment, sex, outcome, counts) ```

step 4 ⋮ Fit the multinomial regression model using the 'multinom' function from the 'nnet' package. The dependent variable is the outcome, and the independent variables are treatment and sex. The R code for fitting the model is:

‖R

step 5

Summarize the fitted model to obtain the coefficients and other statistics. Use the following R code: ```

R summary(model) ""`

Answer

The R code provided in steps 2 to 5 will fit a multinomial regression model with main effects for treatment and sex and summarize the model's results.

Key Concept

Multinomial logistic regression is used to model relationships between a nominal dependent variable with more than two levels and one or more independent variables.

Explanation

The 'multinom' function from the 'nnet' package in R is used to fit the multinomial regression model. The model is summarized to interpret the effects of the independent variables (treatment and sex) on the dependent variable (outcome).