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AMS 315
Data Analysis, Spring 2024
Second Computing Assignment
Multiple Regression Computing Project
Introduction
This assignment is due on Thursday, May 9th, 2024, at 11:59 pm Stony Brook time. Each student is assigned to an individual database, with a single file containing the data. Please goto the Content->Project section, which contains the datafiles. Your file is the one with the last six digits of your Stony Brook identification number. Each file contains one dependent variable and twenty-four 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 should be no missing values; that is, the data file is complete and needs no further processing. This project is worth up to 100 points. Failure to use the correct dataset will lead to a grade of zero. Again, the data sets are identified by the last six digits of your Stony Brook University ID as a csv file. The datasets are posted in a zip format on the class Brightspace.
Background
The class Brightspace (Chapter 12 reading) 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
yi = (500 + 5E1i + 25G2i + 50E3iG4i + 100G5iG6i + 2zi )2
The class Brightspace 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 the 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 ashow 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 you propose 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 Brightspace has an editorial (by Cummings, Reporting Statistical Information) 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 maybe 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 E3 G4 or G5 G6) in generating your data. There may also be non-linear environmental variables, such as E3(2) or E4(0).5 .
The TA may well have used three factor interactions in the models for a few of the students.
Hints
Chapter 12 and Chapter 13 in your textbook 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 Brightspace 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 orR)
(b) Additional information that you want to report
(c) Any comments or suggestions
Practical Advice for Data Analysis Project
1. Scatterplot of Y vs. Ei.
2. T-tests controlling for Gj
3. Correlation coefficients of Y with each IV.
4. Identify a reasonable number (say, about 10) of IVs that appear to have abivariate association with Y.
5. Multiple regression of Yon the IVs (24). Remember Bonferroni’s inequality. I would multiply the p-value of each regression coefficient by 24; the product should be small (say 0.01) for a significant variable.
6. Identify a candidate list of significant variables from this regression.
7. Make sure you consider these variables in your final model.
8. Add your interaction variables. Adding extra variables increases the variance of the
estimated coefficients. Many students have lost important variables due to this increased variance problem.
9. Make sure that you discuss the “big picture” questions. Were there any genetic
associations with the outcome variable? Were there any gene-gene or gene-environment interactions? A number of data sets may have no gene associations. A number may have gene-environment or gene-gene interactions.
Editing your report
Outline your report before you write it.
. Make sure that you have finalized your model and know your findings before you start to write your report.
. You should not use an outline format for your report.
. You should only show output that is fundamental to your findings.
Review your final model with a critical eye.
. We will calculate the number of correct decisions you make about each variable as the starting point of grading your paper.
. Bonferroni’s inequality is a crucial tool in assessing whether or not to include a variable in your final model.
. Type I and Type II errors are always possible.
Suggestions for structuring your report
Introduction
What are the research questions?
• Any associations of Y with G variables
• Any association of Y with GxE variables? GxG?
What is the background of research that this study is based in?
Methods
How much missing data was there?
How did you handle missing data?
What was your research plan?
• Multiple regression with search strategy.
• Did you consider interactions?
• If so, which ones?
• Which interactions did you select?
• How did you account for multiple comparison issues?
Results
Report only your final model.
• You can test whether the G variables in your final model added to the best model found using only E variables.
What variables were associated with Y?
Discussion and Conclusions
What were the answers to your research questions?
What are the limitations of your analysis?
Tables and Figures for your final model only.
If you use a table or figure, you should discuss it.