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Fit a logistic regression of conservative on the linear effects of the volumes of amygdala and acc.

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Project 2

The data set n90_pol.csv contains information on 90 university students who participated in a psychological experiment designed to look for relationships between the size of different regions of the brain and political views. The variables amygdala and acc indicate the volume of two particular brain regions know to be involved in emotions and decision-making, the amygdala and the anterior cingulate cortex; more exactly, these are residuals from the predicted volume, after adjusting for height, sex, and similar body-type variables.   The variable (political) orientation gives the subjects’ scores on a five-point scale from 1 (very conservative) to 5 (very liberal); so orientation is not continuous but an ordinal variable. The goal of the study is to investigate the relationship between brain anatomy and political orientation.  Based on your exploratory and main analysis, summarize your overall conclusion about the relationship.  Specifically, you need to:

In the exploratory analysis, you could ignore the fact that orientation is an ordinal variable and investigate (1) the correlation between orientation and the volume of the amygdala and

(2) the correlation between orientation and the volume of the acc. Also obtain 95% bootstrap confidence intervals for these correlations. You will need to choose a specific bootstrap sam- pling approach and justify your choice. Also, fit a linear regression model for orientation on the volumes of amygdala and acc to get some rough ideas on how the students’ political orientation is related to the volumes at these two brain regions. Present necessary results to support your conclusions.

In the main analysis, create a binary response variable, conservative, which is 1 when the student has orientation ≤ 2, and 0 otherwise.

1. Fit a logistic regression of conservative on the linear effects of the volumes of amygdala and acc.

2. Fit a generalized additive model for conservative on the volumes of amygdala and acc.

For each model, you should evaluate model calibration, interpret the fitted model;  report the in-sample mis-classification rate using the 0.5 cutoff (meaning we predict 1 if the fitted probability is ≥ 0.5 and 0 otherwise); recalculate the classification error rates by using cross- validation (k-fold based on the same splits when comparing different models or leave-one- out). Is the generalized additive model better than the linear logistic regression model? To choose the final model, you need to compare both the model fitting and prediction of the two models using the appropriate tools learned in this course.

Note: Your report needn’t be long, but it should be clear, well-organized, free of grammatical and other mechanical errors, and easy to follow. Figures and tables need to have CAPTIONS and are easy to read, with informative captions, axis labels and legends, and are placed near the text of the corresponding problems. All claims need to be supported by either appropriate derivations or empirical evidence.  Numerical results are reported to appropriate precision.  R code needs to be clearly divided into sections referring to particular problems by adding necessary comments. Include the R code at the end of the report in an appendix. At last, submit the R source code in a script (.r) or a markdown (.rmd).

 

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