Multinomial Logit - Overview. Other Post-Estimation Commands for mlogit. Assignment 6: Paper Proposal - Due March 25, Send copies to both the instructor and the TA. Models for Count Outcomes. 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. Count Models.
Assignment 7: Count Models - Due April 1, 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. Introduction The course outlines lists all the topics covered in Taiwan. We are only doing the first few. Setting up the data. Fixed effects and conditional logit models. Fixed effects versus random effects models. Basic Multilevel models. Assignment 8: Panel Data Methods. Due April 8, 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.
Standardized Coefficients in Logistic Regression. Alternatives to logistic regression. This is actually an older version of the handout but it includes several additional points that might be helpful. Assignment 9: Intermediate issues in logistic regression analysis. Due April 15, 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. Powerpoint version - Also get this handout.
Updates to gologit2 : This describes major updates to the program since it was released in Watch t-test for two independent samples in Stata. Watch t-test for two paired samples in Stata. Watch One sample t-tests calculator. Watch Two sample t-tests calculator. Watch A tour of effect sizes. Watch Introduction to Factor Variables in Stata tutorials. The basics Interactions More interactions.
If some of the scores receive tied ranks, then a correction factor is used, yielding a slightly different value of chi-squared.
With or without ties, the results indicate that there is a statistically significant difference among the three type of programs. A paired samples t-test is used when you have two related observations i. For example, using the hsb2 data file we will test whether the mean of read is equal to the mean of write.
The Wilcoxon signed rank sum test is the non-parametric version of a paired samples t-test. You use the Wilcoxon signed rank sum test when you do not wish to assume that the difference between the two variables is interval and normally distributed but you do assume the difference is ordinal.
We will use the same example as above, but we will not assume that the difference between read and write is interval and normally distributed. The results suggest that there is not a statistically significant difference between read and write. If you believe the differences between read and write were not ordinal but could merely be classified as positive and negative, then you may want to consider a sign test in lieu of sign rank test.
Again, we will use the same variables in this example and assume that this difference is not ordinal. This output gives both of the one-sided tests as well as the two-sided test. These binary outcomes may be the same outcome variable on matched pairs like a case-control study or two outcome variables from a single group. For example, let us consider two questions, Q1 and Q2, from a test taken by students.
Suppose students answered both questions correctly, 15 students answered both questions incorrectly, 7 answered Q1 correctly and Q2 incorrectly, and 6 answered Q2 correctly and Q1 incorrectly. These counts can be considered in a two-way contingency table.
The null hypothesis is that the two questions are answered correctly or incorrectly at the same rate or that the contingency table is symmetric. The outcome is labeled according to case-control study conventions. You would perform a one-way repeated measures analysis of variance if you had one categorical independent variable and a normally distributed interval dependent variable that was repeated at least twice for each subject.
This is the equivalent of the paired samples t-test, but allows for two or more levels of the categorical variable. This tests whether the mean of the dependent variable differs by the categorical variable. In this data set, y is the dependent variable, a is the repeated measure and s is the variable that indicates the subject number. You will notice that this output gives four different p-values. No matter which p-value you use, our results indicate that we have a statistically significant effect of a at the.
If you have a binary outcome measured repeatedly for each subject and you wish to run a logistic regression that accounts for the effect of these multiple measures from each subjects, you can perform a repeated measures logistic regression. In Stata, this can be done using the xtgee command and indicating binomial as the probability distribution and logit as the link function to be used in the model.
The exercise data file contains 3 pulse measurements of 30 people assigned to 2 different diet regiments and 3 different exercise regiments. First, we use xtset to define which variable defines the repetitions. In this dataset, there are three measurements taken for each id , so we will use id as our panel variable.
Then we can use i: before diet so that we can create indicator variables as needed. A factorial ANOVA has two or more categorical independent variables either with or without the interactions and a single normally distributed interval dependent variable. For example, using the hsb2 data file we will look at writing scores write as the dependent variable and gender female and socio-economic status ses as independent variables, and we will include an interaction of female by ses. Note that in Stata, you do not need to have the interaction term s in your data set.
You perform a Friedman test when you have one within-subjects independent variable with two or more levels and a dependent variable that is not interval and normally distributed but at least ordinal. We will use this test to determine if there is a difference in the reading, writing and math scores. The null hypothesis in this test is that the distribution of the ranks of each type of score i. To conduct the Friedman test in Stata, you need to first download the friedman program that performs this test.
You can download friedman from within Stata by typing search friedman see How can I used the search command to search for programs and get additional help? Also, your data will need to be transposed such that subjects are the columns and the variables are the rows. We will use the xpose command to arrange our data this way. Hence, there is no evidence that the distributions of the three types of scores are different.
Ordered logistic regression is used when the dependent variable is ordered, but not continuous. For example, using the hsb2 data file we will create an ordered variable called write3.
This variable will have the values 1, 2 and 3, indicating a low, medium or high writing score. We do not generally recommend categorizing a continuous variable in this way; we are simply creating a variable to use for this example.
We will use gender female , reading score read and social studies score socst as predictor variables in this model. There are two cutpoints for this model because there are three levels of the outcome variable. One of the assumptions underlying ordinal logistic and ordinal probit regression is that the relationship between each pair of outcome groups is the same.
In other words, ordinal logistic regression assumes that the coefficients that describe the relationship between, say, the lowest versus all higher categories of the response variable are the same as those that describe the relationship between the next lowest category and all higher categories, etc. This is called the proportional odds assumption or the parallel regression assumption. Because the relationship between all pairs of groups is the same, there is only one set of coefficients only one model.
If this was not the case, we would need different models such as a generalized ordered logit model to describe the relationship between each pair of outcome groups. To test this assumption, we can use either the omodel command search omodel , see How can I used the search command to search for programs and get additional help? We will show both below. A factorial logistic regression is used when you have two or more categorical independent variables but a dichotomous dependent variable. We will use type of program prog and school type schtyp as our predictor variables.
Because prog is a categorical variable it has three levels , we need to create dummy codes for it. The use of i. Wilcoxon-Mann Whitney test. Chi- square test. Fisher's exact test. Kruskal Wallis. Wilcoxon signed ranks test. Friedman test. Mann Whitney, Wilcoxon rank sum test. Analysis of Covariance General Linear Models regression.
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