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eval:
eval:
eval:
covariate_ij (centered)
covariate_i alter
covariate_i similarity
0.4529
0.1632
0.4147
In the example output, three parameters are restricted. The joint test has test statistic
c, which has under the null hypothesis a chi-squared distribution with d.f. = 3. The pvalue corresponding to the joint test indicates that the restricted model is not tenable.
Looking at the separate tests, it seems that the misfit is due to all three parameters. Thus,
it is sensible to improve the goodness-of-fit of the baseline model by including all of these
parameters, and estimate them.
8.4
Alternative application: convergence problems
An alternative use of the score test statistic is as follows. When convergence of the estimation algorithm is doubtful, it is sensible to restrict the model to be estimated. Either
”problematic” or ”non-problematic” parameters can be kept constant at preliminary estimates (estimated parameters values). Though such strategies may be doubtful in at least
some cases, it may be, in other cases, the only viable option besides simply abandoning
”problematic” models. The test statistic can be exploited as a guide in the process of
restricting and estimating models, as small values of the test statistic indicate that the
imposed restriction on the parameters is not problematic.
8.5
Testing differences between independent groups
Sometimes it is interesting to test differences between parameters estimated for independent groups. For example, for work-related support networks analyzed in two different
firms, one might wish to test whether the tendency to reciprocation of work-related support, as reflected by the reciprocity parameter, is equally strong in both firms. Such a
comparison is meaningful especially if the total model is the same in both groups, as control
for different other effects would compromise the basis of comparison of the parameters.
If the parameter estimates in the two networks are β̂a and β̂b , with standard errors
s.e a and s.e b , respectively, then the difference can be tested with the test statistic
β̂ − β̂b
q a
,
s.e2a + s.e2b
(5)
which under the null hypothesis of equal parameters has an approximating standard normal distribution.
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