> wnba.rcr2 <- lmer(points~ minutes + coppav + home + + (1 + minutes + home + coppav|player_id),REML=TRUE, + control=lmerControl(opt="optimx",optCtrl = list(method="nlminb"))) > > summary(wnba.rcr2) Linear mixed model fit by REML t-tests use Satterthwaite approximations to degrees of freedom [lmerMod] Formula: points ~ minutes + coppav + home + (1 + minutes + home + coppav | player_id) Control: lmerControl(opt = "optimx", optCtrl = list(method = "nlminb")) Random effects: Groups Name Variance Std.Dev. Corr player_id (Intercept) 2.61503 1.6171 minutes 0.01789 0.1338 -0.98 home 1.06870 1.0338 -0.58 0.73 coppav 0.01635 0.1279 -0.54 0.36 -0.37 Residual 18.30502 4.2784 Number of obs: 631, groups: player_id, 20 Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) -3.25293 0.72662 23.56100 -4.477 0.000163 *** minutes 0.49971 0.03900 18.44600 12.814 1.26e-10 *** coppav -0.06108 0.05285 21.05100 -1.156 0.260738 home 0.57415 0.41355 28.85100 1.388 0.175661 Correlation of Fixed Effects: (Intr) minuts coppav minutes -0.883 coppav -0.164 0.151 home -0.355 0.317 -0.095 > (lnL2 <- logLik(wnba.rcr2)) 'log Lik.' -1842.915 (df=15) > vcov(wnba.rcr2) 4 x 4 Matrix of class "dpoMatrix" (Intercept) minutes coppav home (Intercept) 0.527974521 -0.025022018 -0.006291715 -0.106786699 minutes -0.025022018 0.001520706 0.000310404 0.005119461 coppav -0.006291715 0.000310404 0.002793268 -0.002084164 home -0.106786699 0.005119461 -0.002084164 0.171023165 > > > rand(wnba.rcr2) Analysis of Random effects Table: Chi.sq Chi.DF p.value minutes:player_id 17.11 4 0.002 ** home:player_id 6.93 4 0.140 coppav:player_id 2.30 4 0.682 > > wnba.rcr3 <- lmer(points~ minutes + coppav + home + + (0 + minutes + home + coppav|player_id),REML=TRUE, + control=lmerControl(opt="optimx",optCtrl = list(method="nlminb"))) > > summary(wnba.rcr3) Linear mixed model fit by REML t-tests use Satterthwaite approximations to degrees of freedom [lmerMod] Formula: points ~ minutes + coppav + home + (0 + minutes + home + coppav | player_id) Control: lmerControl(opt = "optimx", optCtrl = list(method = "nlminb")) Random effects: Groups Name Variance Std.Dev. Corr player_id minutes 0.005715 0.0756 home 0.981334 0.9906 0.69 coppav 0.017320 0.1316 0.29 -0.49 Residual 18.441293 4.2943 Number of obs: 631, groups: player_id, 20 Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) -2.92393 0.66746 582.20000 -4.381 1.4e-05 *** minutes 0.49310 0.03154 90.10000 15.633 < 2e-16 *** coppav -0.05986 0.05356 20.00000 -1.118 0.277 home 0.56485 0.40891 29.60000 1.381 0.177 Correlation of Fixed Effects: (Intr) minuts coppav minutes -0.786 coppav -0.016 0.083 home -0.214 0.206 -0.130 > (lnL3 <- logLik(wnba.rcr3)) 'log Lik.' -1844.804 (df=11) > vcov(wnba.rcr3) 4 x 4 Matrix of class "dpoMatrix" (Intercept) minutes coppav home (Intercept) 0.4455005014 -0.0165390746 -0.0005772972 -0.058530957 minutes -0.0165390746 0.0009948938 0.0001397647 0.002650985 coppav -0.0005772972 0.0001397647 0.0028683245 -0.002851344 home -0.0585309575 0.0026509854 -0.0028513444 0.167209850 > > (X2.intercept <- -2*(lnL3 - lnL2)) 'log Lik.' 3.777442 (df=11) > (P.X2.intercept <- 1 - pchisq(X2.intercept,4)) 'log Lik.' 0.4369628 (df=11) > wnba.rcr4 <- lmer(points~ minutes + coppav + home + + (0 + minutes|player_id),REML=TRUE, + control=lmerControl(opt="optimx",optCtrl = list(method="nlminb"))) > > summary(wnba.rcr4) Linear mixed model fit by REML t-tests use Satterthwaite approximations to degrees of freedom [lmerMod] Formula: points ~ minutes + coppav + home + (0 + minutes | player_id) Control: lmerControl(opt = "optimx", optCtrl = list(method = "nlminb")) Random effects: Groups Name Variance Std.Dev. player_id minutes 0.008065 0.08981 Residual 18.936503 4.35161 Number of obs: 631, groups: player_id, 20 Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) -3.02526 0.66085 586.00000 -4.578 5.74e-06 *** minutes 0.49626 0.03333 77.40000 14.889 < 2e-16 *** coppav -0.06675 0.04499 613.70000 -1.484 0.138 home 0.57061 0.34746 608.90000 1.642 0.101 Correlation of Fixed Effects: (Intr) minuts coppav minutes -0.739 coppav -0.021 -0.003 home -0.262 0.005 0.024 > (lnL4 <- logLik(wnba.rcr4)) 'log Lik.' -1848.065 (df=6) > vcov(wnba.rcr4) 4 x 4 Matrix of class "dpoMatrix" (Intercept) minutes coppav home (Intercept) 0.4367178436 -1.628390e-02 -6.188087e-04 -6.007691e-02 minutes -0.0162838965 1.110838e-03 -4.942856e-06 5.908905e-05 coppav -0.0006188087 -4.942856e-06 2.023970e-03 3.825496e-04 home -0.0600769081 5.908905e-05 3.825496e-04 1.207272e-01 > > (X2.inthmoppav <- -2*(lnL4 - lnL2)) 'log Lik.' 10.30022 (df=6) > (P.X2.inthmoppav <- 1 - pchisq(X2.inthmoppav,9)) 'log Lik.' 0.3267316 (df=6) > > rand(wnba.rcr4) Analysis of Random effects Table: Chi.sq Chi.DF p.value minutes:player_id 108 1 <2e-16 *** > >