Guidelines for the Final Paper

HUDM 5122

For your final project, you will analyze real data using appropriate regression techniques and draw meaningful conclusions with regard to your research questions. Nowadays, it is actually fairly easy to get your hands on interesting data. Here is a sample of websites where you can find interesting data.

- kaggle

- AWS Open Data

- data.world

- ICPSR

- The Google Dataset Search

- The UCIML Repo

- The CMU data repository

- The datasets subreddit

- Tycho

- Data Portals

The paper should be written in a style. consistent with the major publication outlet in your field (e.g., APA formatting style). Technical description of the regression model (e.g., diagnostics) and SPSS syntax should be included in an appendix. The paper should be written as coherently as possible, as if you were submitting it for publication, and should be submitted online.

1.   The maximum paper number for the paper is 10 pages (double spaced, font size: 12pts). Note that 10 pages are the upper limit. If your analysis turns out to be rather straightforward, you might not need all 10 pages.

2.   However, you may add an Appendix to the 10 pages. The appendix typically contains tables and figures (e.g., residual plots or SPSS-syntax) and should be limited to at most 3 pages.

Pages exceeding the double-spaced 13-page limit will not be read.

3.   Your paper should have the following short sections:

a.   Introduction

b.   Research questions

c.   Description of data used

Provide descriptive statistics for the important variables that you use in your regression model. Tables and plots should be provided if they are useful in describing the data, but they should be limited in 1-3 pages.

d.   The method used

State the formal regression equation (with the βs) of the final model, including the assumptions for the error term. Try to specify a useful model using substantive theories and model diagnostics.

e.   Description of results

f.   Discussion & conclusions (plus references and appendix). For the purpose of this

course’s paper, keep the introduction very short (not more than one page), instead put more emphasis on the correct interpretation of results.

4.   Regarding the formatting style, you are required to adhere to APA guidelines. For a quick

overview see, for instance,APA Formatting and Style Guide.  This particularly requires you  to have nicely formatted tables and figures. Simple “copy & paste”-tables from SPSS (as you did for the weekly assignments) are no longer allowed. Tables have to be formatted according to APA styles (also think about a useful rounding of numbers). You can find online-examples for how regression output translates into tables for publications, for instance at: Regression example.

5.   In writing your report, try to tell the reader an interesting story. In particular, avoid too

technical descriptions of results. For instance, instead of saying that “The regression coefficient for math-anxiety indicates that a one-unit increase in X (independent variable) results in an average decrease in Y (dependent variable) of .5 units. This effect is statistically significant.” you could say “Math-anxiety has a significant negative effect on math-achievement, i.e., if anxiety increases by one point on the anxiety scale the math achievement score drops on average by .5 points”. If you have many variables in your model, you do not need to explain all estimated coefficients but always explain interaction effects and the coefficients of transformed variables (e.g., log-transformed variables), it applicable.

6.   Tips for running the analyses:

a.   Estimate an initial regression model, i.e., a model that is either suggested by a strong substantive theory, a weak theory together with common sense reasoning, or a model that just includes most important covariates as main effect (i.e., without any interaction effects). After you estimate your initial model, run several diagnostic model tests and then try to improve your initial model according to the diagnostic results.

b.   Diagnostic tests and substantive theory might suggest the inclusion of interaction effects, quadratic or cubic effects, or other useful transformations like taking the  logarithm of variables (of heavily right skewed variables or count variables).

c.   You may also want to “down-scale” your continuous variables to categorical variables in case the functional form. between the outcome and the continuous variable is rather complex, i.e., highly non-linear (for instance, in class we “transformed” years of education into 5 different educational degrees). However, before you transform. data or include higher-order terms, always check whether the resulting model is still meaningful in a substantive sense (you should be able to substantively justify your transformations). Keep in mind that the principle is “the simpler, the better.”

d.   In trying to improve your initial model, using an incremental test or adjusted R2  is rather helpful. If you include further variables, interaction effects, or higher-order effects (like a quadratic term), test whether the extended model explains significantly more variation in your outcome than the more parsimonious model. If not, you might consider dropping the corresponding terms. However, if theory suggests for instance a quadratic effect but it is not significant in your model, you should not drop the quadratic term but explain it in the text (saying that your data didn’t support the substantive theory with regard to the expected quadratic effect).

e.   In selecting a “best”-fitting model by running and comparing several models, you conduct an exploratory data analysis. That is, you start with your initial model, include new variables, plausible interactions and other higher-order terms, then drop all or some of them, try other variables, transformations, etc, drop them if they don’t improve the model, and so on. Whenever you estimate a new model, have a quick look at diagnostic statistics because that might always guide you in what to do next  (particularly, plot the residuals against independent variables and the fitted values + add a regression smoother; and use residual plots for getting a rough idea about homoskedasticity and normality of residuals as well as possible outliers).

f.   At some point you need to stop, of course. Note that there is no guarantee that you will succeed in getting a model that meets all testable assumptions. If your final model still violates assumptions, report the violations and be more modest and humbler in interpreting your results. (A note on inferential statistics: Since you are trying to fit a useful model in an exploratory way, i.e., you estimate several models  and pick the model with the best fit among all fitted and meaningful models, type I error rates for testing regression coefficients and testing the overall model no longer hold. Type I error rates are typically larger than the assumed 5% error rate.)

g.   In writing up the paper, do the following: First, only report the final model. There is  no need to report the initial model or models you estimated between the two models. For the final model I require you to state the model equation (i.e., the regression equation with the betas, error term, etc., but also state the assumptions required for estimating and testing regression coefficients). Second, present the regression coefficients and additional statistics like standard errors or the R2  in a table and describe the meaning of the coefficients. In the discussion/conclusion section you should also address whether the required assumptions are met for your model. When assessing assumptions, also think about whether you lack some important predictors (i.e., important variables you would need in your model but that are not available in  the dataset you use). If that is the case, briefly address it.

With regard to the description of results don’t forget to explain the meaning of regression coefficients—if you have many variables in your model, you only need to explain a selection of them, but always explain the meaning of regression coefficients of transformed variables, interaction or higher-order effects. In discussing the assumptions, you should include diagnostic plots/statistics of the final model in the Appendix.