WWS509 - Stata Logs

5 Log-linear Models for Contingency Tables in Stata

In this section we illustrate the use of Stata's poisson command to fit log-linear models to contingency tables.

5.1 Models for Two-dimensional Tables

We start with a two-way table, namely the data on cholesterol and heart disease in Section 5.1 of the lecture notes. Let us read in the four counts with suitable markers for the rows and columns. I will use strings to represent the categories of cholesterol and heart disease.

. input str4 chol str4 hdis n

          chol       hdis          n
  1.    low    yes     51
  2.    low    no     992
  3.    high   yes     41
  4.    high   no     245
  5. end

To fit the model of independence of cholesterol and heart disease we treat the four counts as Poisson observations and fit an additive model. Here are the necessary dummy variables and the fit:

. gen hichol   = chol == "high"

. gen heartdis = hdis  == "yes"

. quietly poisson n hichol heartdis

. poisgof

         Goodness-of-fit chi2  =  26.43064
         Prob > chi2(1)        =    0.0000

The model's deviance or goodness of fit chi-squared is 26.43 on 1 df, as noted on the lecture notes. Let us get the fitted values:

. predict mu
(option n assumed; predicted number of events)

Note that using predict after a Poisson regression calculates the fitted counts.

Pearson's chi-squared statistic can be obtained using the glm command or from first principles as

. gen Pearson = sum( (n-mu)^2/mu )

. display "Pearson's chi2 = " Pearson[_N]
Pearson's chi2 = 31.081829