> fp.mod1 <- aov(tnl ~ fee_trt*expblock + fee_trt:dcc + week:expblock) > summary(fp.mod1) Df Sum Sq Mean Sq F value Pr(>F) fee_trt 1 0.2199 0.21985 130.380 < 2e-16 *** expblock 4 0.1538 0.03846 22.808 4.77e-15 *** fee_trt:expblock 4 0.1400 0.03499 20.749 6.73e-14 *** fee_trt:dcc 8 0.3791 0.04738 28.100 < 2e-16 *** expblock:week 15 0.0714 0.00476 2.825 6e-04 *** Residuals 167 0.2816 0.00169 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > > library(lmerTest) > > fp.mod2 <- lmer(tnl ~ fee_trt*expblock + (1|fee_trt:dcc) + (1|expblock:week)) > summary(fp.mod2) Linear mixed model fit by REML t-tests use Satterthwaite approximations to degrees of freedom [lmerMod] Formula: tnl ~ fee_trt * expblock + (1 | fee_trt:dcc) + (1 | expblock:week) REML criterion at convergence: -602 Scaled residuals: Min 1Q Median 3Q Max -3.5751 -0.5877 0.0988 0.5797 2.5034 Random effects: Groups Name Variance Std.Dev. expblock:week (Intercept) 0.0003077 0.01754 fee_trt:dcc (Intercept) 0.0022848 0.04780 Residual 0.0016863 0.04106 Number of obs: 200, groups: expblock:week, 20; fee_trt:dcc, 10 Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 0.21665 0.02298 13.64000 9.429 2.39e-07 *** fee_trtcontrol 0.02316 0.03358 10.43000 0.690 0.50541 expblockin1 0.04730 0.01716 22.80000 2.757 0.01127 * expblockin2 0.10970 0.01716 22.80000 6.394 1.66e-06 *** expblockin3 0.12728 0.01716 22.80000 7.418 1.61e-07 *** expblockpost 0.11849 0.01716 22.80000 6.906 5.09e-07 *** fee_trtcontrol:expblockin1 -0.05822 0.01874 167.00000 -3.106 0.00223 ** fee_trtcontrol:expblockin2 -0.12172 0.01874 167.00000 -6.494 9.16e-10 *** fee_trtcontrol:expblockin3 -0.13371 0.01874 167.00000 -7.134 2.83e-11 *** fee_trtcontrol:expblockpost -0.14055 0.01874 167.00000 -7.499 3.61e-12 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Correlation of Fixed Effects: (Intr) f_trtc expbl1 expbl2 expbl3 expblc f_tr:1 f_tr:2 f_tr:3 fe_trtcntrl -0.585 expblockin1 -0.373 0.122 expblockin2 -0.373 0.122 0.500 expblockin3 -0.373 0.122 0.500 0.500 expblockpst -0.373 0.122 0.500 0.500 0.500 f_trtcntr:1 0.163 -0.279 -0.437 -0.218 -0.218 -0.218 f_trtcntr:2 0.163 -0.279 -0.218 -0.437 -0.218 -0.218 0.500 f_trtcntr:3 0.163 -0.279 -0.218 -0.218 -0.437 -0.218 0.500 0.500 f_trtcntrl: 0.163 -0.279 -0.218 -0.218 -0.218 -0.437 0.500 0.500 0.500 > anova(fp.mod2) Analysis of Variance Table of type III with Satterthwaite approximation for degrees of freedom Sum Sq Mean Sq NumDF DenDF F.value Pr(>F) fee_trt 0.007824 0.007824 1 8.000 4.6399 0.063374 . expblock 0.035165 0.008791 4 15.445 5.2135 0.007404 ** fee_trt:expblock 0.139950 0.034988 4 167.002 20.7487 6.728e-14 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > if(require(pbkrtest)) + anova(fp.mod2,ddf="Kenward-Roger") Analysis of Variance Table of type III with Kenward-Roger approximation for degrees of freedom Sum Sq Mean Sq NumDF DenDF F.value Pr(>F) fee_trt 0.007824 0.007824 1 8.000 4.6399 0.063374 . expblock 0.035165 0.008791 4 15.445 5.2135 0.007404 ** fee_trt:expblock 0.139950 0.034988 4 167.000 20.7487 6.727e-14 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > lsmeansLT(fp.mod2) Least Squares Means table: fee_trt expblock Estimate Standard Error DF fee_trt latefee 2.0 NA 0.2972 0.0203 8.6 fee_trt control 1.0 NA 0.2295 0.0247 8.4 expblock pre NA 5.0 0.2282 0.0189 15.0 expblock in1 NA 1.0 0.2464 0.0189 15.0 expblock in2 NA 2.0 0.2771 0.0189 15.0 expblock in3 NA 3.0 0.2887 0.0189 15.0 expblock post NA 4.0 0.2764 0.0189 15.0 fee_trt:expblock latefee pre 2.0 5.0 0.2167 0.0230 13.6 fee_trt:expblock control pre 1.0 5.0 0.2398 0.0275 12.7 fee_trt:expblock latefee in1 2.0 1.0 0.2640 0.0230 13.6 fee_trt:expblock control in1 1.0 1.0 0.2289 0.0275 12.7 fee_trt:expblock latefee in2 2.0 2.0 0.3264 0.0230 13.6 fee_trt:expblock control in2 1.0 2.0 0.2278 0.0275 12.7 fee_trt:expblock latefee in3 2.0 3.0 0.3439 0.0230 13.6 fee_trt:expblock control in3 1.0 3.0 0.2334 0.0275 12.7 fee_trt:expblock latefee post 2.0 4.0 0.3351 0.0230 13.6 fee_trt:expblock control post 1.0 4.0 0.2177 0.0275 12.7 t-value Lower CI Upper CI p-value fee_trt latefee 14.67 0.251 0.343 <2e-16 *** fee_trt control 9.31 0.173 0.286 <2e-16 *** expblock pre 12.05 0.188 0.269 <2e-16 *** expblock in1 13.01 0.206 0.287 <2e-16 *** expblock in2 14.63 0.237 0.317 <2e-16 *** expblock in3 15.24 0.248 0.329 <2e-16 *** expblock post 14.59 0.236 0.317 <2e-16 *** fee_trt:expblock latefee pre 9.43 0.167 0.266 <2e-16 *** fee_trt:expblock control pre 8.74 0.180 0.299 <2e-16 *** fee_trt:expblock latefee in1 11.49 0.214 0.313 <2e-16 *** fee_trt:expblock control in1 8.34 0.169 0.288 <2e-16 *** fee_trt:expblock latefee in2 14.20 0.277 0.376 <2e-16 *** fee_trt:expblock control in2 8.30 0.168 0.287 <2e-16 *** fee_trt:expblock latefee in3 14.97 0.294 0.393 <2e-16 *** fee_trt:expblock control in3 8.50 0.174 0.293 <2e-16 *** fee_trt:expblock latefee post 14.59 0.286 0.385 <2e-16 *** fee_trt:expblock control post 7.93 0.158 0.277 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > difflsmeans(fp.mod2) Differences of LSMEANS: Estimate Standard Error DF fee_trt latefee - control 0.1 0.0314 8.0 expblock pre - in1 0.0 0.0155 15.4 expblock pre - in2 0.0 0.0155 15.4 expblock pre - in3 -0.1 0.0155 15.4 expblock pre - post 0.0 0.0155 15.4 expblock in1 - in2 0.0 0.0155 15.4 expblock in1 - in3 0.0 0.0155 15.4 expblock in1 - post 0.0 0.0155 15.4 expblock in2 - in3 0.0 0.0155 15.4 expblock in2 - post 0.0 0.0155 15.4 expblock in3 - post 0.0 0.0155 15.4 fee_trt:expblock latefee pre - control pre 0.0 0.0336 10.4 fee_trt:expblock latefee pre - latefee in1 0.0 0.0172 22.8 fee_trt:expblock latefee pre - control in1 0.0 0.0358 13.1 fee_trt:expblock latefee pre - latefee in2 -0.1 0.0172 22.8 fee_trt:expblock latefee pre - control in2 0.0 0.0358 13.1 fee_trt:expblock latefee pre - latefee in3 -0.1 0.0172 22.8 fee_trt:expblock latefee pre - control in3 0.0 0.0358 13.1 fee_trt:expblock latefee pre - latefee post -0.1 0.0172 22.8 fee_trt:expblock latefee pre - control post 0.0 0.0358 13.1 fee_trt:expblock control pre - latefee in1 0.0 0.0358 13.1 fee_trt:expblock control pre - control in1 0.0 0.0191 34.3 fee_trt:expblock control pre - latefee in2 -0.1 0.0358 13.1 fee_trt:expblock control pre - control in2 0.0 0.0191 34.3 fee_trt:expblock control pre - latefee in3 -0.1 0.0358 13.1 fee_trt:expblock control pre - control in3 0.0 0.0191 34.3 fee_trt:expblock control pre - latefee post -0.1 0.0358 13.1 fee_trt:expblock control pre - control post 0.0 0.0191 34.3 fee_trt:expblock latefee in1 - control in1 0.0 0.0336 10.4 fee_trt:expblock latefee in1 - latefee in2 -0.1 0.0172 22.8 fee_trt:expblock latefee in1 - control in2 0.0 0.0358 13.1 fee_trt:expblock latefee in1 - latefee in3 -0.1 0.0172 22.8 fee_trt:expblock latefee in1 - control in3 0.0 0.0358 13.1 fee_trt:expblock latefee in1 - latefee post -0.1 0.0172 22.8 fee_trt:expblock latefee in1 - control post 0.0 0.0358 13.1 fee_trt:expblock control in1 - latefee in2 -0.1 0.0358 13.1 fee_trt:expblock control in1 - control in2 0.0 0.0191 34.3 fee_trt:expblock control in1 - latefee in3 -0.1 0.0358 13.1 fee_trt:expblock control in1 - control in3 0.0 0.0191 34.3 fee_trt:expblock control in1 - latefee post -0.1 0.0358 13.1 fee_trt:expblock control in1 - control post 0.0 0.0191 34.3 fee_trt:expblock latefee in2 - control in2 0.1 0.0336 10.4 fee_trt:expblock latefee in2 - latefee in3 0.0 0.0172 22.8 fee_trt:expblock latefee in2 - control in3 0.1 0.0358 13.1 fee_trt:expblock latefee in2 - latefee post 0.0 0.0172 22.8 fee_trt:expblock latefee in2 - control post 0.1 0.0358 13.1 fee_trt:expblock control in2 - latefee in3 -0.1 0.0358 13.1 fee_trt:expblock control in2 - control in3 0.0 0.0191 34.3 fee_trt:expblock control in2 - latefee post -0.1 0.0358 13.1 fee_trt:expblock control in2 - control post 0.0 0.0191 34.3 fee_trt:expblock latefee in3 - control in3 0.1 0.0336 10.4 fee_trt:expblock latefee in3 - latefee post 0.0 0.0172 22.8 fee_trt:expblock latefee in3 - control post 0.1 0.0358 13.1 fee_trt:expblock control in3 - latefee post -0.1 0.0358 13.1 fee_trt:expblock control in3 - control post 0.0 0.0191 34.3 fee_trt:expblock latefee post - control post 0.1 0.0336 10.4 t-value Lower CI Upper CI fee_trt latefee - control 2.15 -0.0048 0.1401 expblock pre - in1 -1.17 -0.0512 0.0149 expblock pre - in2 -3.14 -0.0819 -0.0158 expblock pre - in3 -3.89 -0.0935 -0.0274 expblock pre - post -3.10 -0.0813 -0.0152 expblock in1 - in2 -1.97 -0.0637 0.0024 expblock in1 - in3 -2.72 -0.0753 -0.0092 expblock in1 - post -1.93 -0.0631 0.0030 expblock in2 - in3 -0.74 -0.0446 0.0215 expblock in2 - post 0.04 -0.0324 0.0337 expblock in3 - post 0.79 -0.0208 0.0453 fee_trt:expblock latefee pre - control pre -0.69 -0.0976 0.0512 fee_trt:expblock latefee pre - latefee in1 -2.76 -0.0828 -0.0118 fee_trt:expblock latefee pre - control in1 -0.34 -0.0895 0.0650 fee_trt:expblock latefee pre - latefee in2 -6.39 -0.1452 -0.0742 fee_trt:expblock latefee pre - control in2 -0.31 -0.0884 0.0661 fee_trt:expblock latefee pre - latefee in3 -7.42 -0.1628 -0.0918 fee_trt:expblock latefee pre - control in3 -0.47 -0.0940 0.0606 fee_trt:expblock latefee pre - latefee post -6.91 -0.1540 -0.0830 fee_trt:expblock latefee pre - control post -0.03 -0.0784 0.0762 fee_trt:expblock control pre - latefee in1 -0.67 -0.1014 0.0532 fee_trt:expblock control pre - control in1 0.57 -0.0279 0.0497 fee_trt:expblock control pre - latefee in2 -2.42 -0.1638 -0.0092 fee_trt:expblock control pre - control in2 0.63 -0.0268 0.0508 fee_trt:expblock control pre - latefee in3 -2.91 -0.1814 -0.0268 fee_trt:expblock control pre - control in3 0.34 -0.0324 0.0452 fee_trt:expblock control pre - latefee post -2.66 -0.1726 -0.0180 fee_trt:expblock control pre - control post 1.16 -0.0167 0.0609 fee_trt:expblock latefee in1 - control in1 1.04 -0.0393 0.1095 fee_trt:expblock latefee in1 - latefee in2 -3.64 -0.0979 -0.0269 fee_trt:expblock latefee in1 - control in2 1.01 -0.0411 0.1135 fee_trt:expblock latefee in1 - latefee in3 -4.66 -0.1155 -0.0445 fee_trt:expblock latefee in1 - control in3 0.85 -0.0467 0.1079 fee_trt:expblock latefee in1 - latefee post -4.15 -0.1067 -0.0357 fee_trt:expblock latefee in1 - control post 1.29 -0.0311 0.1235 fee_trt:expblock control in1 - latefee in2 -2.72 -0.1748 -0.0202 fee_trt:expblock control in1 - control in2 0.06 -0.0377 0.0399 fee_trt:expblock control in1 - latefee in3 -3.21 -0.1923 -0.0377 fee_trt:expblock control in1 - control in3 -0.24 -0.0433 0.0343 fee_trt:expblock control in1 - latefee post -2.97 -0.1835 -0.0290 fee_trt:expblock control in1 - control post 0.58 -0.0277 0.0499 fee_trt:expblock latefee in2 - control in2 2.94 0.0242 0.1730 fee_trt:expblock latefee in2 - latefee in3 -1.02 -0.0531 0.0179 fee_trt:expblock latefee in2 - control in3 2.60 0.0157 0.1703 fee_trt:expblock latefee in2 - latefee post -0.51 -0.0443 0.0267 fee_trt:expblock latefee in2 - control post 3.03 0.0313 0.1859 fee_trt:expblock control in2 - latefee in3 -3.24 -0.1934 -0.0388 fee_trt:expblock control in2 - control in3 -0.29 -0.0444 0.0332 fee_trt:expblock control in2 - latefee post -3.00 -0.1846 -0.0301 fee_trt:expblock control in2 - control post 0.53 -0.0288 0.0488 fee_trt:expblock latefee in3 - control in3 3.29 0.0361 0.1850 fee_trt:expblock latefee in3 - latefee post 0.51 -0.0267 0.0443 fee_trt:expblock latefee in3 - control post 3.52 0.0489 0.2035 fee_trt:expblock control in3 - latefee post -2.84 -0.1790 -0.0245 fee_trt:expblock control in3 - control post 0.82 -0.0232 0.0544 fee_trt:expblock latefee post - control post 3.50 0.0430 0.1918 p-value fee_trt latefee - control 0.063 . expblock pre - in1 0.260 expblock pre - in2 0.006 ** expblock pre - in3 0.001 ** expblock pre - post 0.007 ** expblock in1 - in2 0.067 . expblock in1 - in3 0.016 * expblock in1 - post 0.072 . expblock in2 - in3 0.468 expblock in2 - post 0.968 expblock in3 - post 0.444 fee_trt:expblock latefee pre - control pre 0.505 fee_trt:expblock latefee pre - latefee in1 0.011 * fee_trt:expblock latefee pre - control in1 0.738 fee_trt:expblock latefee pre - latefee in2 <2e-16 *** fee_trt:expblock latefee pre - control in2 0.760 fee_trt:expblock latefee pre - latefee in3 <2e-16 *** fee_trt:expblock latefee pre - control in3 0.648 fee_trt:expblock latefee pre - latefee post <2e-16 *** fee_trt:expblock latefee pre - control post 0.976 fee_trt:expblock control pre - latefee in1 0.512 fee_trt:expblock control pre - control in1 0.571 fee_trt:expblock control pre - latefee in2 0.031 * fee_trt:expblock control pre - control in2 0.533 fee_trt:expblock control pre - latefee in3 0.012 * fee_trt:expblock control pre - control in3 0.738 fee_trt:expblock control pre - latefee post 0.019 * fee_trt:expblock control pre - control post 0.256 fee_trt:expblock latefee in1 - control in1 0.320 fee_trt:expblock latefee in1 - latefee in2 0.001 ** fee_trt:expblock latefee in1 - control in2 0.331 fee_trt:expblock latefee in1 - latefee in3 1e-04 *** fee_trt:expblock latefee in1 - control in3 0.408 fee_trt:expblock latefee in1 - latefee post 4e-04 *** fee_trt:expblock latefee in1 - control post 0.219 fee_trt:expblock control in1 - latefee in2 0.017 * fee_trt:expblock control in1 - control in2 0.954 fee_trt:expblock control in1 - latefee in3 0.007 ** fee_trt:expblock control in1 - control in3 0.816 fee_trt:expblock control in1 - latefee post 0.011 * fee_trt:expblock control in1 - control post 0.563 fee_trt:expblock latefee in2 - control in2 0.014 * fee_trt:expblock latefee in2 - latefee in3 0.316 fee_trt:expblock latefee in2 - control in3 0.022 * fee_trt:expblock latefee in2 - latefee post 0.614 fee_trt:expblock latefee in2 - control post 0.009 ** fee_trt:expblock control in2 - latefee in3 0.006 ** fee_trt:expblock control in2 - control in3 0.772 fee_trt:expblock control in2 - latefee post 0.010 * fee_trt:expblock control in2 - control post 0.602 fee_trt:expblock latefee in3 - control in3 0.008 ** fee_trt:expblock latefee in3 - latefee post 0.614 fee_trt:expblock latefee in3 - control post 0.004 ** fee_trt:expblock control in3 - latefee post 0.014 * fee_trt:expblock control in3 - control post 0.419 fee_trt:expblock latefee post - control post 0.005 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > vcov(fp.mod2) 10 x 10 Matrix of class "dpoMatrix" (Intercept) fee_trtcontrol expblockin1 (Intercept) 5.279878e-04 -4.510664e-04 -1.471819e-04 fee_trtcontrol -4.510664e-04 1.127666e-03 7.026052e-05 expblockin1 -1.471819e-04 7.026052e-05 2.943637e-04 expblockin2 -1.471819e-04 7.026052e-05 1.471819e-04 expblockin3 -1.471819e-04 7.026052e-05 1.471819e-04 expblockpost -1.471819e-04 7.026052e-05 1.471819e-04 fee_trtcontrol:expblockin1 7.026052e-05 -1.756513e-04 -1.405210e-04 fee_trtcontrol:expblockin2 7.026052e-05 -1.756513e-04 -7.026052e-05 fee_trtcontrol:expblockin3 7.026052e-05 -1.756513e-04 -7.026052e-05 fee_trtcontrol:expblockpost 7.026052e-05 -1.756513e-04 -7.026052e-05 expblockin2 expblockin3 expblockpost (Intercept) -1.471819e-04 -1.471819e-04 -1.471819e-04 fee_trtcontrol 7.026052e-05 7.026052e-05 7.026052e-05 expblockin1 1.471819e-04 1.471819e-04 1.471819e-04 expblockin2 2.943637e-04 1.471819e-04 1.471819e-04 expblockin3 1.471819e-04 2.943637e-04 1.471819e-04 expblockpost 1.471819e-04 1.471819e-04 2.943637e-04 fee_trtcontrol:expblockin1 -7.026052e-05 -7.026052e-05 -7.026052e-05 fee_trtcontrol:expblockin2 -1.405210e-04 -7.026052e-05 -7.026052e-05 fee_trtcontrol:expblockin3 -7.026052e-05 -1.405210e-04 -7.026052e-05 fee_trtcontrol:expblockpost -7.026052e-05 -7.026052e-05 -1.405210e-04 fee_trtcontrol:expblockin1 (Intercept) 7.026052e-05 fee_trtcontrol -1.756513e-04 expblockin1 -1.405210e-04 expblockin2 -7.026052e-05 expblockin3 -7.026052e-05 expblockpost -7.026052e-05 fee_trtcontrol:expblockin1 3.513026e-04 fee_trtcontrol:expblockin2 1.756513e-04 fee_trtcontrol:expblockin3 1.756513e-04 fee_trtcontrol:expblockpost 1.756513e-04 fee_trtcontrol:expblockin2 (Intercept) 7.026052e-05 fee_trtcontrol -1.756513e-04 expblockin1 -7.026052e-05 expblockin2 -1.405210e-04 expblockin3 -7.026052e-05 expblockpost -7.026052e-05 fee_trtcontrol:expblockin1 1.756513e-04 fee_trtcontrol:expblockin2 3.513026e-04 fee_trtcontrol:expblockin3 1.756513e-04 fee_trtcontrol:expblockpost 1.756513e-04 fee_trtcontrol:expblockin3 (Intercept) 7.026052e-05 fee_trtcontrol -1.756513e-04 expblockin1 -7.026052e-05 expblockin2 -7.026052e-05 expblockin3 -1.405210e-04 expblockpost -7.026052e-05 fee_trtcontrol:expblockin1 1.756513e-04 fee_trtcontrol:expblockin2 1.756513e-04 fee_trtcontrol:expblockin3 3.513026e-04 fee_trtcontrol:expblockpost 1.756513e-04 fee_trtcontrol:expblockpost (Intercept) 7.026052e-05 fee_trtcontrol -1.756513e-04 expblockin1 -7.026052e-05 expblockin2 -7.026052e-05 expblockin3 -7.026052e-05 expblockpost -1.405210e-04 fee_trtcontrol:expblockin1 1.756513e-04 fee_trtcontrol:expblockin2 1.756513e-04 fee_trtcontrol:expblockin3 1.756513e-04 fee_trtcontrol:expblockpost 3.513026e-04