> spat.mod1 <- lmer(shovtime ~ length*angle + (1|subject) + (1|subject:length) + + (1|subject:angle)) > summary(spat.mod1) Linear mixed model fit by REML t-tests use Satterthwaite approximations to degrees of freedom [ merModLmerTest] Formula: shovtime ~ length * angle + (1 | subject) + (1 | subject:length) + (1 | subject:angle) REML criterion at convergence: 672.2 Scaled residuals: Min 1Q Median 3Q Max -2.1473 -0.5351 0.0073 0.5667 2.8923 Random effects: Groups Name Variance Std.Dev. subject:angle (Intercept) 0.01819 0.1349 subject:length (Intercept) 0.63906 0.7994 subject (Intercept) 52.85968 7.2705 Residual 13.07619 3.6161 Number of obs: 128, groups: subject:angle, 32; subject:length, 32; subject, 8 Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 75.150 2.885 10.670 26.047 5.31e-11 *** length2 -1.500 1.852 83.460 -0.810 0.42021 length3 -0.370 1.852 83.460 -0.200 0.84211 length4 4.730 1.852 83.460 2.554 0.01245 * angle2 -5.920 1.809 84.000 -3.272 0.00155 ** angle3 -3.000 1.809 84.000 -1.658 0.10103 angle4 1.950 1.809 84.000 1.078 0.28422 length2:angle2 3.520 2.557 63.000 1.377 0.17350 length3:angle2 2.990 2.557 63.000 1.169 0.24667 length4:angle2 2.240 2.557 63.000 0.876 0.38434 length2:angle3 -0.750 2.557 63.000 -0.293 0.77024 length3:angle3 1.120 2.557 63.000 0.438 0.66287 length4:angle3 3.520 2.557 63.000 1.377 0.17350 length2:angle4 1.050 2.557 63.000 0.411 0.68273 length3:angle4 3.070 2.557 63.000 1.201 0.23439 length4:angle4 1.120 2.557 63.000 0.438 0.66287 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Correlation of Fixed Effects: (Intr) lngth2 lngth3 lngth4 angle2 angle3 angle4 lng2:2 lng3:2 lng4:2 lng2:3 lng3:3 length2 -0.321 length3 -0.321 0.500 length4 -0.321 0.500 0.500 angle2 -0.314 0.488 0.488 0.488 angle3 -0.314 0.488 0.488 0.488 0.500 angle4 -0.314 0.488 0.488 0.488 0.500 0.500 lngth2:ngl2 0.222 -0.690 -0.345 -0.345 -0.707 -0.353 -0.353 lngth3:ngl2 0.222 -0.345 -0.690 -0.345 -0.707 -0.353 -0.353 0.500 lngth4:ngl2 0.222 -0.345 -0.345 -0.690 -0.707 -0.353 -0.353 0.500 0.500 lngth2:ngl3 0.222 -0.690 -0.345 -0.345 -0.353 -0.707 -0.353 0.500 0.250 0.250 lngth3:ngl3 0.222 -0.345 -0.690 -0.345 -0.353 -0.707 -0.353 0.250 0.500 0.250 0.500 lngth4:ngl3 0.222 -0.345 -0.345 -0.690 -0.353 -0.707 -0.353 0.250 0.250 0.500 0.500 0.500 lngth2:ngl4 0.222 -0.690 -0.345 -0.345 -0.353 -0.353 -0.707 0.500 0.250 0.250 0.500 0.250 lngth3:ngl4 0.222 -0.345 -0.690 -0.345 -0.353 -0.353 -0.707 0.250 0.500 0.250 0.250 0.500 lngth4:ngl4 0.222 -0.345 -0.345 -0.690 -0.353 -0.353 -0.707 0.250 0.250 0.500 0.250 0.250 lng4:3 lng2:4 lng3:4 length2 length3 length4 angle2 angle3 angle4 lngth2:ngl2 lngth3:ngl2 lngth4:ngl2 lngth2:ngl3 lngth3:ngl3 lngth4:ngl3 lngth2:ngl4 0.250 lngth3:ngl4 0.250 0.500 lngth4:ngl4 0.500 0.500 0.500 > anova(spat.mod1) Analysis of Variance Table of type 3 with Satterthwaite approximation for degrees of freedom Sum Sq Mean Sq NumDF DenDF F.value Pr(>F) length 816.35 272.116 3 21 20.8101 1.701e-06 *** angle 862.64 287.546 3 21 21.9900 1.106e-06 *** length:angle 113.28 12.587 9 63 0.9626 0.4791 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > step(spat.mod1) Random effects: Chi.sq Chi.DF elim.num p.value subject:angle 0.00 1 1 0.9876 subject:length 0.27 1 2 0.6013 subject 148.86 1 kept <1e-07 Fixed effects: Sum Sq Mean Sq NumDF DenDF F.value elim.num Pr(>F) length:angle 113.2814 12.5868 9 105 0.9254 1 0.5064 length 975.9361 325.3120 3 114 24.0583 kept <1e-07 angle 867.4383 289.1461 3 114 21.3836 kept <1e-07 Least squares means: length angle Estimate Standard Error DF t-value Lower CI Upper CI p-value length 1 1.0 NA 73.41 2.65 7.7 27.6 67.2 79.6 <2e-16 *** length 2 2.0 NA 72.86 2.65 7.7 27.4 66.7 79.0 <2e-16 *** length 3 3.0 NA 74.83 2.65 7.7 28.2 68.7 81.0 <2e-16 *** length 4 4.0 NA 79.86 2.65 7.7 30.1 73.7 86.0 <2e-16 *** angle 1 NA 1.0 75.86 2.65 7.7 28.6 69.7 82.0 <2e-16 *** angle 2 NA 2.0 72.13 2.65 7.7 27.2 66.0 78.3 <2e-16 *** angle 3 NA 3.0 73.84 2.65 7.7 27.8 67.7 80.0 <2e-16 *** angle 4 NA 4.0 79.12 2.65 7.7 29.8 73.0 85.3 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Differences of LSMEANS: Estimate Standard Error DF t-value Lower CI Upper CI p-value length 1 - 2 0.5 0.919 114.0 0.59 -1.276 2.366 0.55 length 1 - 3 -1.4 0.919 114.0 -1.55 -3.246 0.396 0.12 length 1 - 4 -6.5 0.919 114.0 -7.02 -8.271 -4.629 <2e-16 *** length 2 - 3 -2.0 0.919 114.0 -2.14 -3.791 -0.149 0.03 * length 2 - 4 -7.0 0.919 114.0 -7.61 -8.816 -5.174 <2e-16 *** length 3 - 4 -5.0 0.919 114.0 -5.47 -6.846 -3.204 <2e-16 *** angle 1 - 2 3.7 0.919 114.0 4.06 1.911 5.554 1e-04 *** angle 1 - 3 2.0 0.919 114.0 2.21 0.206 3.849 0.03 * angle 1 - 4 -3.3 0.919 114.0 -3.55 -5.081 -1.439 6e-04 *** angle 2 - 3 -1.7 0.919 114.0 -1.85 -3.526 0.116 0.07 . angle 2 - 4 -7.0 0.919 114.0 -7.61 -8.814 -5.171 <2e-16 *** angle 3 - 4 -5.3 0.919 114.0 -5.75 -7.109 -3.466 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Final model: lme4::lmer(formula = shovtime ~ length + angle + (1 | subject), REML = reml.lmerTest.private, contrasts = l.lmerTest.private.contrast, devFunOnly = devFunOnly.lmerTest.private)