> mod1 <- lm(auc ~ seq + seq/subject + period + trt + carry) > anova(mod1) Analysis of Variance Table Response: auc Df Sum Sq Mean Sq F value Pr(>F) seq 5 32059489 6411898 14.7241 7.171e-08 *** period 2 554361 277180 0.6365 0.5349859 trt 2 9239256 4619628 10.6084 0.0002388 *** carry 2 1235351 617675 1.4184 0.2553037 seq:subject 15 111941046 7462736 17.1372 4.682e-12 *** Residuals 36 15676876 435469 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > mod2 <- lm(auc ~ seq + seq/subject + period + carry + trt) > anova(mod2) Analysis of Variance Table Response: auc Df Sum Sq Mean Sq F value Pr(>F) seq 5 32059489 6411898 14.7241 7.171e-08 *** period 2 554361 277180 0.6365 0.5349859 carry 2 2436392 1218196 2.7974 0.0742555 . trt 2 8038215 4019107 9.2294 0.0005811 *** seq:subject 15 111941046 7462736 17.1372 4.682e-12 *** Residuals 36 15676876 435469 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > > mod3 <- lmer(auc ~ seq + period + trt + carry + + (1|subject:seq)) fixed-effect model matrix is rank deficient so dropping 1 column / coefficient > summary(mod3) fixed-effect model matrix is rank deficient so dropping 1 column / coefficient fixed-effect model matrix is rank deficient so dropping 1 column / coefficient fixed-effect model matrix is rank deficient so dropping 1 column / coefficient Linear mixed model fit by REML t-tests use Satterthwaite approximations to degrees of freedom [merModLmerTest] Formula: auc ~ seq + period + trt + carry + (1 | subject:seq) REML criterion at convergence: 876.9 Scaled residuals: Min 1Q Median 3Q Max -2.28823 -0.37693 0.00809 0.45919 1.81340 Random effects: Groups Name Variance Std.Dev. subject:seq (Intercept) 2342423 1530.5 Residual 435469 659.9 Number of obs: 63, groups: subject:seq, 21 Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 3915.89 928.48 16.20 4.218 0.000638 *** seq2 -512.88 1208.97 15.22 -0.424 0.677334 seq3 1163.70 1204.61 15.00 0.966 0.349344 seq4 -752.54 1291.87 15.19 -0.583 0.568762 seq5 -459.74 1291.87 15.19 -0.356 0.726829 seq6 947.07 1208.97 15.22 0.783 0.445432 period2 -14.45 270.30 36.00 -0.053 0.957665 period3 215.08 270.30 36.00 0.796 0.431416 trt2 -407.77 229.45 36.00 -1.777 0.083988 . trt3 -981.15 229.45 36.00 -4.276 0.000134 *** carry1 110.28 307.84 36.00 0.358 0.722268 carry2 -383.62 307.84 36.00 -1.246 0.220757 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Correlation of Fixed Effects: (Intr) seq2 seq3 seq4 seq5 seq6 perid2 perid3 trt2 trt3 seq2 -0.745 seq3 -0.741 0.569 seq4 -0.697 0.538 0.533 seq5 -0.692 0.534 0.533 0.500 seq6 -0.739 0.571 0.569 0.534 0.538 period2 -0.053 -0.048 0.000 -0.045 -0.045 -0.048 period3 -0.053 -0.048 0.000 -0.045 -0.045 -0.048 0.716 trt2 -0.131 0.027 0.000 0.025 -0.010 -0.011 -0.073 -0.073 trt3 -0.102 -0.011 0.000 -0.010 -0.036 -0.038 0.218 0.218 0.500 carry1 -0.008 0.042 0.000 0.040 0.079 0.085 -0.569 -0.569 -0.128 -0.447 carry2 -0.071 0.085 0.000 0.079 0.040 0.042 -0.569 -0.569 0.319 -0.128 carry1 seq2 seq3 seq4 seq5 seq6 period2 period3 trt2 trt3 carry1 carry2 0.500 > anova(mod3) fixed-effect model matrix is rank deficient so dropping 1 column / coefficient fixed-effect model matrix is rank deficient so dropping 1 column / coefficient fixed-effect model matrix is rank deficient so dropping 1 column / coefficient fixed-effect model matrix is rank deficient so dropping 1 column / coefficient fixed-effect model matrix is rank deficient so dropping 1 column / coefficient fixed-effect model matrix is rank deficient so dropping 1 column / coefficient Analysis of Variance Table of type 3 with Satterthwaite approximation for degrees of freedom Sum Sq Mean Sq NumDF DenDF F.value Pr(>F) seq 2089778 417956 5 15.176 0.9598 0.4721518 period 553175 553175 2 36.000 1.2703 0.2671673 trt 8038215 4019107 2 36.000 9.2294 0.0005811 *** carry 1235351 617675 2 36.000 1.4184 0.2553037