Fall 2024 [In Progress]
NOTE: My Stata Highlights page includes links to Stata and statistical handouts from my other courses that may interest readers.
Last Year's Notes: Click here if you want to see the complete online notes and handouts from the last time the course was taught. I will be making some changes this year; but the old notes should be fine for anyone who wants to get a head start on methods we haven't gotten to yet. Links on this page will become "live" once the handout is ready.
Stata is in the labs. You can also order your own personal copy of Stata through the GradPlan package. Stata Student Pricing is especially cheap. Stata 17 is now out and I encourage you to get it if you want to work off campus. Alternatively you can use the Online Virtual Labs. If you need something more powerful you can check out How to Use Stata on the Notre Dame Center for Resource Computing (CRC) Machines. These use Unix and can be accessed remotely over the web. I'd much rather have you use the online virtual machines or the CRC machines instead of some hand-me-down old version of Stata that has bugs that were fixed years ago or which lacks important new features.
NOTE: The following special types of files are used on this web page. Some materials are available only to nd.edu users.
Pdf files. Require Adobe Acrobat.
Stata files.
Useful sites for learning about Stata and SPSS
Links to major topics on this page
[Overview] [Review of Continuous Models] [GLMs, MLE] [Basics of logistic regression]
[[Adjusted Predictions and Marginal Effects] [Complex Survey Designs] [Missing Data]
[Ordinal Outcomes I] [Multinomial Outcomes] [Ordinal Independent Variables]
[Intermediate Logistic Regression] [Nested Models]
[Panel Data/ Multilevel Models]
[Group Comparisons/Hetero Choice] [gologit models]
[Count Outcomes] [Rare Events] [Fractional Response Models]
This course discusses methods and models for the analysis of categorical dependent variables and their applications in social science research. Researchers are often interested in the determinants of categorical outcomes. For example, such outcomes might be binary (lives/dies), ordinal (very likely/ somewhat likely/ not likely, nominal (taking the bus, car, or train to work) or count (the number of times something has happened, such as the number of articles written). When dependent variables are categorical rather than continuous, conventional OLS regression techniques are not appropriate. This course therefore discusses the wide array of methods that are available for examining categorical outcomes.
Regression Models for Categorical Dependent Variables Using Stata (required text; as far as I know it is cheapest to order directly from the Stata Bookstore)
Fixed Effects Regression Models, by Paul Allison. (required text; order it from Amazon or elsewhere). Notre Dame users can also access an e-version from our library.
Stata Files Stata data files used in the course will usually be stored in this folder.
Recommended Reading (ND.Edu Netid is required for access)
Cloud Storage. I strongly urge you to use something like Dropbox, Google Drive, Microsoft Onedrive, Box, or a similar service to back up your most critical files. With so many free and inexpensive services now available, there is really no excuse for losing more than a day's work, if that. I am very fond of Dropbox but just about anything will do. For more options see Notre Dame Collaboration and File Storage.
Useful Research Resources for Notre Dame Students. ND students can get free/low cost newspaper subscriptions and free online access to millions of research articles. I find these resources incredibly helpful to me in my work. Be sure to check them out!
Basic Dataset Exploration & File Preparation. You should get to know your dataset before you start to analyze it. This handout includes suggestions for using dataset documentation; documenting your own work; Using fre instead of tab1for frequencies; Including options with tab2; coding missing data correctly; converting string variables to numeric variables; Creating Binary or Ordinal Variables from Continuous Measures; Handling More Complicated Data Structures; and Other Useful Resources. The PDF file is bookmarked so you can easily skip to the sections you are interested in. This handout may be especially helpful when doing Homework #1. Here is the do file if you want to replicate its analyis.
A Note on the Treatment of Gender and Race in My Statistics Notes. [DRAFT] Early versions of some of my statistics handouts first saw life more than 30 years ago. There have been many changes in statistical practice and preferred wording over those 30 years. My notes (and for that matter probably most of my publications) reflect common past practices. As I update handouts, I am making changes to reflect current, more inclusive terminology. The handout also lists several resources for those who are interested in studying often-overlooked gender identities such as transgender and non-binary.
Brief Review of Models for Continuous Outcomes (Review this on your own and come to me with questions as needed)
I. Foundations of categorical data analysis.
This section will go over the basics of logistic regression. It will also go over techniques for making results more interpretable; analyzing data sets with complex sampling schemes; and (possibly) techniques for handling missing data. I call these topics "foundations" because once you understand them it is very easy to extend them to other CDA methods.
Overview of Generalized Linear Models, Maximum Likelihood Estimation
Models for Binomial Outcomes: Basics of Logistic Regression
(Optional) Paul Allison further elaborates on the merits of the logit model. However, Paul von Hippel maintains the LPM often isn't so bad. Allison responds back. Marc Bellamare, Christopher Zorn, Dave Giles, and Marc Bellamare (again) further debate the issue. My own feeling is that the best of both worlds is to use logit and then couple it with marginal effects.
Assignment 2: Basics of Logistic Regression.
Due Sept 19
Interpreting results: Adjusted Predictions and Marginal effects
The results from binomial and ordinal models can often be difficult to interpret. All too often, researchers discuss the sign and statistical significance of results but say little about their substantive significance. I will expect every student paper to use the methods described in this section and/or one of the advanced methods we discuss later in the course. I will also expect students to be familiar with some of Long & Freese's spost13 commands, such as mtable and mchange. I will probably go over the first handout fairly carefully and then skim the rest, since they are mostly examples you can go over on your own.
Margins01 and Margins03 will definitely be covered in class. The others you should read on your own and ask questions if you have them.
Also - the Stata Journal article I wrote on this is available for free. For an application of the margins command, see my 2013 article with Lutz Bornmann entitled How to calculate the practical significance of citation impact differences? The do file and data file required to replicate the paper's analysis are here.
Assignment 3: Interpreting
results: Adjusted Predictions and Marginal Effects.
Due Sept 26
Categorical Data Analysis with Complex Survey Designs
By default, most statistical techniques assume that data were collected via simple random sampling. This is often not true for large national data sets. Fortunately, Stata makes it easy to analyze such data, but there are some important differences in how you go about testing hypotheses and assessing model fit.
Also worth seeing: UCLA's (see lower third of page) and StataCorp's FAQS on Survey Data Analysis. Also Chuck Huber has an excellent video on Specifying the design of your survey data in Stata. (But if your dataset is as complicated as the one in his example, you'd better hope that the study documentation is really clear on how to do things.)
I am mostly covering this here because it is an important topic and there wasn't enough time to cover it in the new Stats I! But, several of the methods do involve the use of categorical data analysis, so it isn't totally out of place. Also, since you are analyzing your own data this semester, you are more likely to have to deal with missing data.
Also worth seeing: The Wisconsin Social Science Computing Cooperative has some great pages on MI. Also possibly helpful are the Statacorp FAQs on MI and this page from UCLA.
Assignment 4: Complex survey Designs; Multiple
Imputation.
Due Oct 3
II. Intermediate CDA Methods
Here we will talk about other commonly used CDA methods, including ordinal regression and models for multinomial outcomes.
Models for Ordinal Outcomes I: The ordered logit and interval regression models
CDA Students: We will work through the Williams and Quiroz paper on Ordinal Regression Models. pp. 1-18 (The ordered logit/ proportional odds model) and pp. 23-26 (interval regression) are required. ND.Edu users can access the entire paper here. If the paper is unclear, you may also want to look at the older handouts listed below -- they cover less territory but provide more of a blow by blow description of what is being done. The do file required to replicate most of the paper's analysis is sageord.do.
For those not at ND: If your library has purchased Sage Research Methods Foundations (and if it hasn't it should!) the entry can be found at https://methods.sagepub.com/Foundations/ordinal-regression-models. [If you want the paper and can't otherwise access it, you can email me at rwilliam@nd.edu for a copy.]
Also Available to Anyone: While I think the Williams/Quiroz paper is better, older handouts and do files that were incorporated into the paper are available at ologit01, intreg2, ologit1.do, and intreg2.do
Everyone: After reading any of the above you will also want to look at the Margins05 handout if you haven't already.
(Optional): It doesn't have much to do with statistics, but here is the true story of the engineer who tried to save Challenger.
Models for Multinomial Outcomes
When categories are unordered, Multinomial Logistic regression is one often-used strategy. We will discuss several ways to aid in the interpretation and testing of these models.
We often want to use ordinal variables as independent/explanatory variables in our models. Rightly or wrongly, it is very common to treat such variables as continuous. The readings discuss when it is appropriate to do so. They also discuss other possible strategies that can be employed with ordinal independent variables.
CDA Students: We will work through the short Williams paper on Ordinal Independent Variables.
For those not at ND: If your library has purchased Sage Research Methods Foundations (and if it hasn't it should!) the entry can be found at https://methods.sagepub.com/Foundations/ordinal-independent-variables . [If you want the paper and can't otherwise access it, you can email me at rwilliam@nd.edu for a copy.]
Also Available to Anyone: While I think the Williams paper is better, the older handout and do files that were incorporated into the paper are available at OrdinalIndependent.pdf and OrdinalIndependentVars.do. The handout includes a few things (e.g. Sheaf Coefficients) I decided not to include in the paper.
Assignment 5: Ordinal and
Multinomial Models Due Oct 10
Assignment 6: Paper Proposal - Due Oct 18
Models for Binary Outcomes II: Intermediate Logistic Regression
Models for Binary Outcomes III: Comparing logit and probit coefficients across nested models
Prelude to Comparing Logit & Probit
Coefficients Between Nested Models
Nested01.do - Stata program for
Prelude to comparing coefficients across nested models
CDA Students: I am going to show you my Sage video!!! We will also work through the short Williams & Jorgensen paper that the video is based on, Comparing logit & probit coefficients between nested models.
For those not at ND: If your library has purchased Sage Research Methods Videos (and if it hasn't it should!) the entry can be found at https://methods.sagepub.com/video/comparing-logit-and-probit-coefficients-between-nested-models . The paper is at https://www.sciencedirect.com/science/article/pii/S0049089X22001132 [If you want the paper and can't otherwise access it, you can email me at rwilliam@nd.edu for a copy.]
Replication Materials: Everything needed to replicate the analysis in the paper is contained in SSR2023Appendix. Also, you can download the following files into a directory where Stata can find them: hypothetical.do, nested.ado, and Obama2008.do.
Also Available to Anyone: The earlier handouts that were eventually incorporated into the published paper are Comparing Logit & Probit Coefficients Between Models (click here for Powerpoint version) and Comparing Logit & Probit Coefficients Between Nested Models (Extended Version). (The latter is actually an older version of the handout but it includes several additional points that might be helpful.)
Assignment 7: Intermediate issues in logistic regression analysis. Due Oct 31
Hw07.do - do file used in HW # 7
III. Advanced Topics (Subject to Change or Re-Ordering)
Sometimes the same individuals (or nations, or companies) are measured at multiple points in time. The statistical technique used needs to reflect the fact that the different measurements are not independent of each other. This is a big topic and goes well beyond Categorical Data Analysis, but a few basic commands, e.g. xtlogit, will be discussed.
NOTE: I AM ACTUALLY GOING TO USE SOME OF THE NOTES FOR A MINI-COURSE I TAUGHT DURING SUMMER 2018 IN TAIWAN. THE COMPLETE SET OF NOTES FROM THAT CLASS ARE HERE.
Also recommended:
http://stats.idre.ucla.edu/stata/dae/mixed-effects-logistic-regression/ (NOTE: xtmelogit has been superceded by melogit)
Assignment 8: Panel Data Methods. Due Nov 14
NOTE: I've covered enough to give you some basic competency with Panel and Multilevel Models, but the Taiwan page has a lot more if you want it. Hybrid models are a way of estimating both fixed and random effects in the same model (albeit with some limitations). You can do adjusted predictions and marginal effects with random effects models. This far-from-finished presentation and handout show an application of many multilevel model methods, including random slopes models. You can do panel data linear models too. Sometimes you are not interested with whether an event occurs, but how quickly (e.g. what factors make people die more quickly?) In such cases, Discrete Time Methods for Event History Analysis can sometimes be a good way to go.
Models for Ordinal Outcomes II: Heterogeneous Choice Models and Other Methods for Comparing Logit & Probit Coefficients Across Groups
To the surprise of many, techniques used for group comparisons in OLS regression (e.g. adding interaction effects) can be highly problematic in logistic and ordinal regression. As Hoetker notes, "in the presence of even fairly small differences in residual variation, naive comparisons of coefficients [across groups] can indicate differences where none exist, hide differences that do exist, and even show differences in the opposite direction of what actually exists." We will discuss how heterogeneous choice models and possibly other methods offer possible solutions. The handout covers only the most critical points; for those who want to know more, the article by Allison and the two articles by Williams that are mentioned and the article by Mize, Doan and Long that are mentioned in the handout are highly recommended.
Models for Ordinal Outcomes III: Generalized ordered logit models
The assumptions of the ordered logit model are often violated. The generalized ordered logit model (estimated by gologit2) sometimes provides a viable but still parsimonious alternative.
For more detail, you should read the 2006 Stata Journal article that introduced the program and the 2016 Journal of Mathematical Sociology article on how to interpret results. The JMS reading requires an nd.edu accout to access; others can find it described at http://www.tandfonline.com/doi/full/10.1080/0022250X.2015.1112384.
With both of the above, the handout on Adjusted predictions and marginal effects for multiple outcome commands and models is again very helpful.
Assignment 9: Advanced issues/ models for ordinal outcomes. Due Nov 21
Variables that count the # of times something happens are common in the Social Sciences. For example, Long examined the # of publications by scientists. Count variables are often treated as though they are continuous and the linear regression model is applied; but this can result in inefficient, inconsistent and biased estimates. In this section we will examine some of the many models that deal explicitly with count outcomes.
Assignment 10: Count Models - Due Nov 28.
IV. Special Topics (Time Permitting)
Models for Binary/Proportional Outcomes IV
