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Statistics for current covariance components model: deviation = 13636-795; number of estimated parameters = 4.

Test of homogeneity of level-1 variance: chi-square statistic = 72-286; number of degrees of freedom = 69; p-value = 0-370

Statistics for current covariance components model: deviation = 13636-795; number of estimated parameters = 4.

Test of homogeneity of level-1 variance: chi-square statistic = 72-286; number of degrees of freedom = 69; p-value = 0-370

Schwarz's Bayesian criterion (BIC). AIC can be used to compare models with the same fixed effects but different covariance structures. Larger values of the AIC indicate better models. Schwarz's BIC is used for the same purpose and is interpreted in the same manner (that is, larger values indicate better models). However, the two criteria are computed in slightly different ways (for example, Schwarz's BIC involves a larger penalty in models with more covariance parameters) and may lead to different conclusions. We can also use a likelihood ratio test to compare models which are submodels of other models by taking — 2 times the difference in log-likelihoods which follows ax2 distribution with p degrees of freedom, where p reflects the difference in the number of parameters estimated between the two models. SAS automatically generates — 2 times the log-likelihood for each model. We use these criteria to compare different models. We now describe estimates and hypothesis tests for fixed effects, covariance components and random effects from HLM/2L and SAS Proc Mixed.

Fixed Effects. Both HLM/2L and SAS Proc Mixed produce similar estimates of the fixed effects and covariance components. For example, the overall adjusted mean satisfaction score is estimated as f0o = 67-9796 by HLM/2L and y0o = 67-9852 by SAS. Physician's years in medical practice has little effect on this overall adjusted mean; the regression coefficient associated with the level 2 covariate, physician's years in medical practice, is estimated as y0i = — 00476 by HLM/2L and y01 = - 0-0474 by SAS (p = 0-688 and p = 0-6896 respectively). There is a significant positive association between patient's age and satisfaction with care. The overall slope coefficient relating the level 1 covariate, patient's age, to satisfaction with care is estimated as yl0 = 0-1476 by both HLM/2L and SAS (p = 0 013 and p = 0-0150, respectively). Patient's age is

Table VI. Intercept and slopes as outcomes model: SAS Proc Mixed

Covariance parameter estiomates (REML)

Cov Parm Subject Estimate Standard Z Pr>|Z|

error

UN(1,1)

phys

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