# st: interpreting wald chi2 for -xtgee- models

 From "Moliterno, Thomas" To Subject st: interpreting wald chi2 for -xtgee- models Date Sun, 28 Mar 2004 11:39:08 -0800

```I'm hoping for some help in interpreting the Wald Chi2 statistic output
for -xtgee- models.  Below is a longish description of my question.
Thanks in advance for any insight, or direction to the relevant
resources/references ... I've checked the Stata manuals, and have come
up dry.

I know that chi2 is a goodness of fit measure (and it's significant in
all my models). Below I give you output (headers only) from 5 models: 1
x controls, 3 x controls plus a single I.V., and 1 x full model. The
models show "(22)" after the chi2 stat, which I take to be the d.f. Now,
two things are puzzling:

1) it seems that the d.f. is based on inter-year periods and not
variables in the model. there are 21 interyear periods but 25 variables
in my models ... So is the chi2 a measure of the variation from period
to period?? You would expect a chi2 squared stat to compare to the
difference in two distributions, so maybe that's how to interpret it ...
the inter-period differences across the sample? Is this right??

2) I'm getting HUGE differences in the values:
a) control: 227.98
b) control + one I.V. (ie., 3 different models): 227.98, 323.79, 2035.13
c) Full Model (controls and all 3 I.V.s): 692.60

What do I make of this? While I would expect, of course, some
improvement in model fit with addition of the I.V.s, is it "reasonable"
to have the chi2 jumping around this much?? All I'm adding is one
variable in each case (except, of course, the full model).

OUTPUT:

a) CONTROL ONLY:
. xtgee PerYEInnTr AttendL PerMSTrade NPitch pitchpark_C
year1969-year1988 if e(sample), i(adj_teamno) t(year) corr(ar5) robust
GEE population-averaged model Number of obs = 496
Group and time vars: adj_teamno year Number of groups = 24
Link: identity Obs per group: min = 13
Family: Gaussian avg = 20.7
Correlation: AR(5) max = 21
Wald chi2(22) = 227.98
Scale parameter: .011506 Prob > chi2 = 0.0000

b) CONTROL + PerInc_67L I.V.:
. xtgee PerYEInnTr PerInc_67L AttendL PerMSTrade NPitch pitchpark_C
GEE population-averaged model Number of obs = 496
Group and time vars: adj_teamno year Number of groups = 24
Link: identity Obs per group: min = 13
Family: Gaussian avg = 20.7
Correlation: AR(5) max = 21
Wald chi2(22) = 323.79
Scale parameter: .0113685 Prob > chi2 = 0.0000

c) CONTROL + t_w_pct I.V.:
xtgee PerYEInnTr t_w_pct AttendL PerMSTrade NPitch pitchpark_C
year1969-year1988 if e(sample), i(adj_teamno) t(year) corr(ar5) robust
GEE population-averaged model Number of obs = 496
Group and time vars: adj_teamno year Number of groups = 24
Link: identity Obs per group: min = 13
Family: Gaussian avg = 20.7
Correlation: AR(5) max = 21
Wald chi2(22) = 2035.13
Scale parameter: .0112536 Prob > chi2 = 0.0000

d)CONTROL + PostFA I.V.:
xtgee PerYEInnTr PostFA AttendL PerMSTrade NPitch pitchpark_C
year1969-year1988 if e(sample), i(adj_teamno) t(year) corr(ar5) robust
note: year1976 dropped due to collinearity
GEE population-averaged model Number of obs = 496
Group and time vars: adj_teamno year Number of groups = 24
Link: identity Obs per group: min = 13
Family: Gaussian avg = 20.7
Correlation: AR(5) max = 21
Wald chi2(22) = 227.98
Scale parameter: .011506 Prob > chi2 = 0.0000

e) FULL MODEL:
xtgee PerYEInnTr t_w_pct PostFA PerInc_67L AttendL PerMSTrade NPitch
pitchpark_C year1969-year1988 if e(sample), i(adj_teamno) t(year)
corr(ar5) robust
note: year1976 dropped due to collinearity
GEE population-averaged model Number of obs = 496
Group and time vars: adj_teamno year Number of groups = 24
Link: identity Obs per group: min = 13
Family: Gaussian avg = 20.7
Correlation: AR(5) max = 21
Wald chi2(22) = 692.60
Scale parameter: .0111595 Prob > chi2 = 0.0000

*****************************************
Thomas P. Moliterno
University of California, Irvine
tmoliter@uci.edu
www.gsm.uci.edu/~tmoliter
*****************************************

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