> fit.cs <- gls(lbrow ~ time, + corr = corCompSymm(, form= ~ 1 | patnum) ) > summary(fit.cs) Generalized least squares fit by REML Model: lbrow ~ time Data: NULL AIC BIC logLik 1182.343 1196.928 -585.1714 Correlation Structure: Compound symmetry Formula: ~1 | patnum Parameter estimate(s): Rho 0.2508621 Coefficients: Value Std.Error t-value p-value (Intercept) 357.9659 34.66024 10.327854 0.0000 time.L 258.9672 45.32134 5.714023 0.0000 time.Q 60.8409 45.32134 1.342434 0.1831 time.C -13.2843 45.32134 -0.293113 0.7702 Correlation: (Intr) time.L time.Q time.L 0 time.Q 0 0 time.C 0 0 0 Standardized residuals: Min Q1 Med Q3 Max -1.9956470 -0.4905372 -0.2035808 0.4414464 4.4497209 Residual standard error: 245.6027 Degrees of freedom: 88 total; 84 residual > anova(fit.cs) Denom. DF: 84 numDF F-value p-value (Intercept) 1 106.6646 <.0001 time 3 11.5127 <.0001 > AIC(fit.cs) [1] 1182.343 > > fit.un <- gls(lbrow ~ time, + corr=corSymm(form = ~ 1 | patnum), + weights = varIdent(form = ~ 1 | time)) > summary(fit.un) Generalized least squares fit by REML Model: lbrow ~ time Data: NULL AIC BIC logLik 1129.131 1163.162 -550.5655 Correlation Structure: General Formula: ~1 | patnum Parameter estimate(s): Correlation: 1 2 3 2 0.669 3 0.451 0.517 4 0.209 0.235 0.445 Variance function: Structure: Different standard deviations per stratum Formula: ~1 | time Parameter estimates: 1 2 3 4 1.000000 1.219558 2.143505 4.149460 Coefficients: Value Std.Error t-value p-value (Intercept) 357.9659 34.66006 10.327907 0.0000 time.L 258.9672 61.47013 4.212894 0.0001 time.Q 60.8409 40.98252 1.484558 0.1414 time.C -13.2843 26.53194 -0.500690 0.6179 Correlation: (Intr) time.L time.Q time.L 0.767 time.Q 0.443 0.769 time.C 0.041 0.255 0.623 Standardized residuals: Min Q1 Med Q3 Max -1.4109335 -0.7650935 -0.2381349 0.6510508 3.0745201 Residual standard error: 99.646 Degrees of freedom: 88 total; 84 residual > anova(fit.un) Denom. DF: 84 numDF F-value p-value (Intercept) 1 116.44287 <.0001 time 3 8.46788 1e-04 > AIC(fit.un) [1] 1129.131 > > fit.ar1 <- gls(lbrow ~ time, + corr = corAR1(, form= ~ 1 | patnum)) > summary(fit.ar1) Generalized least squares fit by REML Model: lbrow ~ time Data: NULL AIC BIC logLik 1177.15 1191.735 -582.5749 Correlation Structure: AR(1) Formula: ~1 | patnum Parameter estimate(s): Phi 0.487248 Coefficients: Value Std.Error t-value p-value (Intercept) 357.9659 38.50009 9.297793 0.0000 time.L 258.9672 54.01587 4.794280 0.0000 time.Q 60.8409 41.08406 1.480889 0.1424 time.C -13.2843 34.21312 -0.388280 0.6988 Correlation: (Intr) time.L time.Q time.L 0.000 time.Q -0.172 0.000 time.C 0.000 -0.140 0.000 Standardized residuals: Min Q1 Med Q3 Max -1.9317305 -0.4748263 -0.1970605 0.4273078 4.3072055 Residual standard error: 253.7292 Degrees of freedom: 88 total; 84 residual > anova(fit.ar1) Denom. DF: 84 numDF F-value p-value (Intercept) 1 94.02320 <.0001 time 3 8.41991 1e-04 > AIC(fit.ar1) [1] 1177.15 > > fit.arh1 <- gls(lbrow ~ time, + corr = corAR1(, form = ~ 1 | patnum), weight = varIdent(form = ~ 1 | time)) > summary(fit.arh1) Generalized least squares fit by REML Model: lbrow ~ time Data: NULL AIC BIC logLik 1120.987 1142.865 -551.4937 Correlation Structure: AR(1) Formula: ~1 | patnum Parameter estimate(s): Phi 0.5502772 Variance function: Structure: Different standard deviations per stratum Formula: ~1 | time Parameter estimates: 1 2 3 4 1.000000 1.241476 2.330034 4.513057 Coefficients: Value Std.Error t-value p-value (Intercept) 357.9659 36.21277 9.885075 0.0000 time.L 258.9672 65.39668 3.959944 0.0002 time.Q 60.8409 39.73588 1.531133 0.1295 time.C -13.2843 24.70635 -0.537687 0.5922 Correlation: (Intr) time.L time.Q time.L 0.823 time.Q 0.457 0.712 time.C 0.038 0.201 0.593 Standardized residuals: Min Q1 Med Q3 Max -1.4084282 -0.7854253 -0.2312973 0.6645366 3.2129481 Residual standard error: 95.35281 Degrees of freedom: 88 total; 84 residual > anova(fit.arh1) Denom. DF: 84 numDF F-value p-value (Intercept) 1 137.07245 <.0001 time 3 6.36435 6e-04 > AIC(fit.arh1) [1] 1120.987 > >