AMS 315
Data Analysis, Fall 2021
Multiple Regression Computing Project

Introduction

This assignment is due on Tuesday, November 23, 2021, at 11:50 pm Stony
Brook time. Extensions will be granted, but remember the last class is December 2.

Each student is assigned to an individual database, with a single file containing
the data. Each file contains one dependent variable and twenty independent variables.
The values of the dependent variable are in the Y column (first column on the left). The
values of the twenty-four independent variables are in the columns with names of E1 to
E4 and G1 to G20. There are no missing values; that is, the data file is complete and
needs no further processing. This project is worth up to 200 points. Failure to use the
correct dataset will lead to a grade of zero. The data sets are named by the last five digits
of your Stony Brook University ID as a csv file. The datasets will be posted in a zip
format on the class blackboard.

Background

The class blackboard has a pdf file of a paper by Caspi et al. that reports a finding
of a gene-environment interaction. This paper used multiple regression techniques as the
methodology for its findings. You should read it for background, as it is the genesis of the
models that you will be given. The data that you are analyzing is synthetic. That is, the
TA used a model to generate the data. Your task is to find the model that the TA used for
your data. For example, one possible model is
2
654321 )210050255500( iiiiiiii ZGGGEGEY +++++= .

The class blackboard also contains a paper by Risch et al. that uses a larger
collection of data to assess the findings in Caspi et al. These researchers confirmed that
Caspi et al. calculated their results correctly but that no other dataset had the relation
reported in Caspi et al. That is, Caspi et al. seem to have reported a false positive (Type I
error).

Report

The report that you submit should be no more than 2500 words with no more than
3 tables and 2 figures. It should include references (which do not count in the 2500
words). The report may have a technical appendix. The appendix could include your
computer programs or describe your procedures for computation. You should include
whatever additional material you feel is necessary to report your results in the technical
appendix. There are no length restrictions on the appendix. A submission of only
computer output without a report is not sufficient and will receive a grade of zero.
Analyses that report an incorrect number of observations will also receive a grade of zero.

Your report should be in standard scientific report format. It should contain an
introduction, methods section, results section, and a section with conclusions and
discussion. You may add whatever other material you wish in a technical appendix. The
introduction should contain the statement of your problem (namely estimating the
function that the TA used to generate your data). It should discuss the context of finding
GxE interactions, as given by Caspi et al. and others. The methods section should discuss
how you performed your statistical calculations, what independent variables that you
considered, and other methodological issues, such as how you dealt with interaction
variables. The results section should contain an objective statement of your findings. That
is, it should contain the statement of the model that your group proposes for the data, the
analysis of variance table for this model, and other key summary results. The discussion
and conclusion section should include the limitations of your procedures. The class
blackboard has an editorial (by Cummings) that discusses reporting statistical information.

Guidelines for analysis

The first task for this problem is to use the statistical package of your choice to
find the correlations between the independent variables and the dependent variable.
Transformations of variables may be necessary. The Box-Cox transformation may find
potentially nonlinear transformations of a dependent variable. After selecting the
transformations of the dependent variable, you may use stepwise regression methods to
select the important independent variables. The Lasso technique was helpful to many
groups in past semesters. The TA will usually use at most two-way interactions of the
independent variables (that is, terms like
21GE or 43GG ) in generating your data. There
may also be non-linear environmental variables, such as 23E or
5.0
4E . The TA may well
have used three factor interactions in the models for a few of the groups.

Hints

Chapter 12 and Chapter 13 in your text contain important information, especially
Chapter 12. Also remember to consider multiple testing issues (as described in Chapter 9).
The p-value for the variables that you select should be much smaller than 0.01.
Remember that you have 4 environmental variables, 20 gene indicator variables, 80 gene-
environment variables, 190 gene-gene interaction variables, and a very large number of
three gene interaction variables. The class blackboard has a handout describing one
approach to analyzing a data set like the one in this assignment.

Your technical appendix may include:
(a) Your SAS or R script (If you are using SAS or R)
(b) Additional information that you want to report
(c) Any comments or suggestions

End of Project Assignment