# PC labs for Winter School Unit 2: Categorical Data Analysis

## 1 Lab 1

### 1.1 Measures of association

#### 1.1.1 Tables and Chi-squared

This is data showing the relation between class of origin and highest educational qualification for a UK sample in 2001:

Social Class of Origin and Whether has Degree

|         univ
class |        No        Yes |     Total
-------------------+----------------------+----------
Prof/Man |     2,333      1,025 |     3,358
Routine non-manual |     1,400        124 |     1,524
Skilled manual |       947         31 |       978
Semi/unskilled |     1,077         18 |     1,095
-------------------+----------------------+----------
Total |     5,757      1,198 |     6,955

Social Class of Origin and Qualification

|               qual
class |      Univ  2nd level  Incomplet |     Total
-------------------+---------------------------------+----------
Prof/Man |      1025       1566        767 |      3358
Routine non-manual |       124        687        713 |      1524
Skilled manual |        31        483        464 |       978
Semi/unskilled |        18        361        716 |      1095
-------------------+---------------------------------+----------
Total |      1198       3097       2660 |      6955

Source: British Household Panel Survey 2001


Use the first panel to calculate the odds ratio (use a calculator or a spreadsheet) comparing prof/man versus semi/unskilled in their chances of having compared with not having a university education. Interpret it.

Do the same for routine-non-manual versus semi/unskilled and skilled versus semi/unskilled. Is there a pattern in the three ORs?

Enter the table in Stata:

input class qual count
1 1 1025
1 2 1566
1 3 767
2 1 124
2 2 687
2 3 713
3 1 31
3 2 483
3 3 464
4 1 18
4 2 361
4 3 716
end

label define cl  1 "Prof/Man" ///
2 "Routine non-manual" ///
3 "Skilled manual" ///
4 "Semi/unskilled"
label define ql  1 "Univ"  2 "2nd level" 3 "Incomplete 2nd"
label values class cl
label values qual ql

// We can get the table using weights
tab class qual [freq=count]

// Or we can "expand" the data (watch out for n=0)
expand count

tab class qual

• Analyse the pattern of percentages (tab class qual, row)
• Compare the observed and expected values – use the Stata add-on, tabchi class qual
• Use tabchi with the res and adj options to generate the raw and adjusted residuals; examine these
• Run the $$\chi^2$$ test and interpret, (tab class qual [freq=count], chi)
• Run and interpret the gamma test (tab class qual [freq=count], gamma)
• What does it tell you? Compare with the pattern of association shown in the percentages with the gamma,and consider which gives you the better summary.

### 1.2 Logistic Regression

#### 1.2.1 Binary logistic regression: Shuttle disaster data

The following data represents measurements of o-ring failures in Space Shuttle launches (an o-ring failure caused one shuttle to explode shortly after launch, and the suspicion was that weather conditions were partly responsible for the failure. The data are air temperature (in degrees F) and whether or not there was o-ring damage.

 T y/n T y/n T y/n 66 0 70 0 5 7 1 72 0 76 0 5 3 1 70 1 69 0 7 6 0 75 0 70 0 6 7 0 75 1 67 0 6 3 1 70 1 81 0 6 7 0 73 0 58 1 7 9 0 78 0 68 0

Source: Agresti & Finlay 3rd edition, q15.4

input temp failure
66  0
70  0
57  1
72  0
76  0
53  1
70  1
69  0
76  0
75  0
70  0
67  0
75  1
67  0
63  1
70  1
81  0
67  0
73  0
58  1
79  0
78  0
68  0
end


Fit a binary logistic regression with temperature as the explanatory variable, and answer the following questions:

1. Report the regression equation, specifying what the effect of temperature is
2. Test the hypothesis that temperature has an effect on failure
3. Calculate the predicted probability of failure at 32°F, 60°F and 75°F
4. At what temperature is the predicted probability of failure 50 percent?

### 1.3 Odds ratios and parameter estimates

Use the command

do http://teaching.sociology.ul.ie/ws/dpind.do


to load a small data set that looks at race and sentences in capital murder cases, from the US. It breaks down whether the death penalty was handed down, by race of defendent and victim.

Calculate the overall odds ratio for white vs black defendents, and then fit a logistic regression with defendent's race as the explanatory variable. Calculate the odds ratio from the regression coefficient and compare with the one you already calculated.

Repeat the exercise for white victims only:

tab def pen if vic==1
logit pen def if vic==1


Note what happens when you do the same for black victims.

## 2 Lab 2: Logistic Regression continued

### 2.1 Classification table

With the credit-card data used in Agresti & Finlay, fit a logistic regression and use estat class to generate the classification table.

do http://teaching.sociology.ul.ie/ws/creditcard.do
logit card income
estat class


Compare the results with those for the null model (i.e., no explanatory variables).

### 2.2 Binary logistic continued

#### 2.2.1 Getting to university

Data from the British Household Panel Survey covering educational qualifications and some potential predictor variables, are available with the following command:

use http://teaching.sociology.ul.ie/ws/data/bhpsqual, clear


Explore the data set and find a good model to predict having a university qualification. Consider using a non-linear formulation of age. Interpret the results.

Generate and interpret the Hosmer-Lemeshow statistic:

logit univ i.sex c.age##c.age // One possible model, can you find a better one?
estat gof, group(10)


Does this model "fit"?

## 3 Lab 3 Multinomial and Ordinal Logistic Regression

### 3.1 Multinomial and ordinal logistic regression

#### 3.1.1 Multinomial logistic regression

Use the following command to load the BHPS excerpt:

use http://teaching.sociology.ul.ie/ws/data/bhpsqual


vote has four categories. Examine bivariate relationships between vote and some of the other variables, and then fit a multinomial logistic regession:

mlogit vote income i.sex, baseoutcome(1)


I suggest using baseoutcome(1) to make "Conservative" the base category, as the default would be the highest category, "Nationalist/Other", which is too mixed. Search for a good model, and interpret it.

Using the variables in your model, select two or three "typical" cases and generate predicted values for them.

Repeat the exercise using qual as the dependent variable.

#### 3.1.2 Ordinal logistic regression

qual is an ordinal variable. In your previous analysis, did you observe patterns in the parameter estimates? Fit a proportional odds model with syntax such as the following:

ologit qual i.sex age


Compare the ordinal logistic results with the multinomial results you have already produced. Do they tell the same story?

For one or two "typical" persons, calculate the predicted probabilities of being "higher" rather than "lower" across the three contrasts.

#### 3.1.3 Probit and logistic regression

Search for a reasonable logistic model predicting having a university qualification. Repeat the exercise using probit regression (replace logit with probit in the estimation command). What differences do you see? Do they matter?

Use Stata to generate predicted values from each model, and compare them.

Date: January 15-16 2018

Created: 2018-01-15 Mon 13:37

Emacs 26.0.50 (Org mode 8.2.10)

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