> #Part 1: Preliminary analyses > > library(readxl) > > #Read Data_wide > DW <- read_excel("C:/Users/bes11qw/Desktop/Arbeitsplatz/EPSY/PUBLIZIEREN/2021_Betz/Publikation/Revision1/Data.xlsx", sheet = "Data_wide") > View(DW) > > #Preliminary tests: gender differences > dw1 <- subset(DW, (Gender == 1)|(Gender == 2)) > t.test(Em_high ~ Gender, data=dw1) Welch Two Sample t-test data: Em_high by Gender t = 5.1709, df = 76.239, p-value = 1.822e-06 alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0 95 percent confidence interval: 0.9515971 2.1437992 sample estimates: mean in group 1 mean in group 2 4.408163 2.860465 > t.test(Em_med ~ Gender, data=dw1) Welch Two Sample t-test data: Em_med by Gender t = -1.3845, df = 81.961, p-value = 0.17 alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0 95 percent confidence interval: -0.7945653 0.1424533 sample estimates: mean in group 1 mean in group 2 2.836735 3.162791 > t.test(Em_low ~ Gender, data=dw1) Welch Two Sample t-test data: Em_low by Gender t = -4.4278, df = 91.86, p-value = 2.621e-05 alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0 95 percent confidence interval: -1.7696259 -0.6736584 sample estimates: mean in group 1 mean in group 2 1.755102 2.976744 > t.test(Mean_Em ~ Gender, data=dw1) Welch Two Sample t-test data: Mean_Em by Gender t = 5.546, df = 77.099, p-value = 3.946e-07 alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0 95 percent confidence interval: 0.1865965 0.3956430 sample estimates: mean in group 1 mean in group 2 1.566531 1.275411 > t.test(Eat_Meat ~ Gender, data=dw1) Welch Two Sample t-test data: Eat_Meat by Gender t = 3.7476, df = 90.007, p-value = 0.0003149 alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0 95 percent confidence interval: 0.3177441 1.0347002 sample estimates: mean in group 1 mean in group 2 4.020408 3.344186 > t.test(Dine_Meat ~ Gender, data=dw1) Welch Two Sample t-test data: Dine_Meat by Gender t = 3.9916, df = 69.887, p-value = 0.0001599 alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0 95 percent confidence interval: 0.4088113 1.2253605 sample estimates: mean in group 1 mean in group 2 2.877551 2.060465 > t.test(Dine_Out ~ Gender, data=dw1) Welch Two Sample t-test data: Dine_Out by Gender t = 2.2009, df = 68.764, p-value = 0.0311 alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0 95 percent confidence interval: 0.03762909 0.76692716 sample estimates: mean in group 1 mean in group 2 3.183673 2.781395 > > #Correlational analyses: emission category, CO2 equivalents, age, frequency of having meat, frequency of having meat in restaurants, frequency of eating in restaurants > corrdata <- data.frame(DW$Em_high, DW$Em_med, DW$Em_low, DW$Mean_Em, DW$Age, DW$Eat_Meat, DW$Dine_Meat, DW$Dine_Out) > cor(corrdata) DW.Em_high DW.Em_med DW.Em_low DW.Mean_Em DW.Age DW.Eat_Meat DW.Dine_Meat DW.Dine_Out DW.Em_high 1.00000000 -0.36467532 -0.69110303 0.94839528 0.13694878 0.53882454 0.38662717 0.03071903 DW.Em_med -0.36467532 1.00000000 -0.42095524 -0.11295788 -0.07984500 0.14792388 0.18620760 0.09338184 DW.Em_low -0.69110303 -0.42095524 1.00000000 -0.83621702 -0.07143458 -0.63972549 -0.52117594 -0.10240942 DW.Mean_Em 0.94839528 -0.11295788 -0.83621702 1.00000000 0.11862418 0.60150359 0.46011661 0.06525445 DW.Age 0.13694878 -0.07984500 -0.07143458 0.11862418 1.00000000 0.07867604 0.06713571 -0.08472116 DW.Eat_Meat 0.53882454 0.14792388 -0.63972549 0.60150359 0.07867604 1.00000000 0.59869777 0.07884024 DW.Dine_Meat 0.38662717 0.18620760 -0.52117594 0.46011661 0.06713571 0.59869777 1.00000000 0.65991077 DW.Dine_Out 0.03071903 0.09338184 -0.10240942 0.06525445 -0.08472116 0.07884024 0.65991077 1.00000000 > > > #Read Data_long > DL <- read_excel("C:/Users/bes11qw/Desktop/Arbeitsplatz/EPSY/PUBLIZIEREN/2021_Betz/Publikation/Revision1/Data.xlsx", sheet = "Data_long") > View(DL) > #Part 2: Multinomial logit models for dish choice > > #Open mlogit package and generate choice alternative-level data > library(mlogit) > packageVersion("mlogit") [1] ‘1.1.1’ > Dc <- dfidx(DL, shape="wide", choice="Emission_Cat", idx="Choice_ID") > head(Dc) ~~~~~~~ first 10 observations out of 7155 ~~~~~~~ Case_ID Labeling Restaurant Default DefaultH DefaultL Field_Chosen Emission_Cat Em_high Em_med Em_low Emission_kgCO2e 1 60 1 1 1 1 0 1 TRUE 1 0 0 2.00 2 60 1 1 1 1 0 1 FALSE 1 0 0 2.00 3 60 1 1 1 1 0 1 FALSE 1 0 0 2.00 4 60 1 2 0 0 0 1 FALSE 0 1 0 1.49 5 60 1 2 0 0 0 1 TRUE 0 1 0 1.49 6 60 1 2 0 0 0 1 FALSE 0 1 0 1.49 7 60 1 3 0 0 0 3 TRUE 1 0 0 1.87 8 60 1 3 0 0 0 3 FALSE 1 0 0 1.87 9 60 1 3 0 0 0 3 FALSE 1 0 0 1.87 10 60 1 4 0 0 0 2 TRUE 1 0 0 1.29 Age Education Occupation Gender GenderM Diet Eat_Meat Dine_Meat Dine_Out idx 1 22 5 4 1 1 2 6 4 4 1:1 2 22 5 4 1 1 2 6 4 4 1:2 3 22 5 4 1 1 2 6 4 4 1:3 4 22 5 4 1 1 2 6 4 4 2:1 5 22 5 4 1 1 2 6 4 4 2:2 6 22 5 4 1 1 2 6 4 4 2:3 7 22 5 4 1 1 2 6 4 4 3:1 8 22 5 4 1 1 2 6 4 4 3:2 9 22 5 4 1 1 2 6 4 4 3:3 10 22 5 4 1 1 2 6 4 4 4:1 ~~~ indexes ~~~~ Choice_ID id2 1 1 1 2 1 2 3 1 3 4 2 1 5 2 2 6 2 3 7 3 1 8 3 2 9 3 3 10 4 1 indexes: 1, 2 > > #Baseline model with person- and item-level random effects > m0 <- mlogit(Emission_Cat ~ 0|Case_ID + Restaurant, Dc, reflevel = "2") > summary(m0) Call: mlogit(formula = Emission_Cat ~ 0 | Case_ID + Restaurant, data = Dc, reflevel = "2", method = "nr") Frequencies of alternatives:choice 2 1 3 0.34465 0.35010 0.30524 nr method 4 iterations, 0h:0m:0s g'(-H)^-1g = 2.48E-06 successive function values within tolerance limits Coefficients : Estimate Std. Error z-value Pr(>|z|) (Intercept):1 6.8391e-02 1.4481e-01 0.4723 0.6367226 (Intercept):3 -6.1752e-01 1.5578e-01 -3.9641 7.366e-05 *** Case_ID:1 -3.7498e-05 9.7396e-05 -0.3850 0.7002309 Case_ID:3 1.3557e-04 1.0149e-04 1.3358 0.1816250 Restaurant:1 -2.9568e-03 1.9074e-02 -0.1550 0.8768120 Restaurant:3 6.9554e-02 1.9845e-02 3.5049 0.0004568 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Log-Likelihood: -2605.8 McFadden R^2: 0.0038317 Likelihood ratio test : chisq = 20.046 (p.value = 0.00048904) > > #Adding default variation and labeling > m1 <- mlogit(Emission_Cat ~ 0|Case_ID + Restaurant + Labeling + DefaultH + DefaultL, Dc, reflevel = "2") > summary(m1) Call: mlogit(formula = Emission_Cat ~ 0 | Case_ID + Restaurant + Labeling + DefaultH + DefaultL, data = Dc, reflevel = "2", method = "nr") Frequencies of alternatives:choice 2 1 3 0.34465 0.35010 0.30524 nr method 4 iterations, 0h:0m:0s g'(-H)^-1g = 0.00468 successive function values within tolerance limits Coefficients : Estimate Std. Error z-value Pr(>|z|) (Intercept):1 8.4722e-02 1.4784e-01 0.5731 0.5666105 (Intercept):3 -8.1914e-01 1.6254e-01 -5.0398 4.661e-07 *** Case_ID:1 -6.0544e-05 9.8838e-05 -0.6126 0.5401711 Case_ID:3 1.5836e-04 1.0380e-04 1.5256 0.1270994 Restaurant:1 -6.5418e-03 2.3920e-02 -0.2735 0.7844797 Restaurant:3 4.7639e-03 2.3616e-02 0.2017 0.8401362 Labeling:1 -2.4954e-01 5.0141e-02 -4.9768 6.465e-07 *** Labeling:3 1.4205e-01 5.2791e-02 2.6908 0.0071271 ** DefaultH:1 4.0149e-01 1.3554e-01 2.9621 0.0030552 ** DefaultH:3 1.9921e-01 1.5554e-01 1.2808 0.2002691 DefaultL:1 -5.3759e-01 1.4871e-01 -3.6151 0.0003002 *** DefaultL:3 1.0274e+00 1.4390e-01 7.1395 9.366e-13 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Log-Likelihood: -2471.2 McFadden R^2: 0.055298 Likelihood ratio test : chisq = 289.3 (p.value = < 2.22e-16) > scoretest(m0, m1) score test data: Emission_Cat ~ 1 - 1 | Case_ID + Restaurant + Labeling + DefaultH + DefaultL chisq = 264.87, df = 6, p-value < 2.2e-16 alternative hypothesis: unconstrained model > > #Effect sizes (increases/decreases of choice likelihood) for default variation and labeling > effects(m1, covariate = "Labeling") 2 1 3 0.01577757 -0.07030861 0.05453104 > effects(m1, covariate = "DefaultH") 2 1 3 -0.071321042 0.070216748 0.001104294 > effects(m1, covariate = "DefaultL") 2 1 3 -0.0434780 -0.2238218 0.2672998 > > #Adding interactions between default variation and labeling > m2 <- mlogit(Emission_Cat ~ 0|Case_ID + Restaurant + Labeling*(DefaultH + DefaultL), Dc, reflevel = "2") > summary(m2) Call: mlogit(formula = Emission_Cat ~ 0 | Case_ID + Restaurant + Labeling * (DefaultH + DefaultL), data = Dc, reflevel = "2", method = "nr") Frequencies of alternatives:choice 2 1 3 0.34465 0.35010 0.30524 nr method 4 iterations, 0h:0m:0s g'(-H)^-1g = 6.42E-07 gradient close to zero Coefficients : Estimate Std. Error z-value Pr(>|z|) (Intercept):1 9.0341e-02 1.4817e-01 0.6097 0.542044 (Intercept):3 -7.9433e-01 1.6286e-01 -4.8774 1.075e-06 *** Case_ID:1 -6.3220e-05 9.9128e-05 -0.6378 0.523628 Case_ID:3 1.6037e-04 1.0388e-04 1.5438 0.122640 Restaurant:1 -5.2516e-03 2.4000e-02 -0.2188 0.826792 Restaurant:3 3.7767e-03 2.3650e-02 0.1597 0.873123 Labeling:1 -2.5772e-01 8.0620e-02 -3.1967 0.001390 ** Labeling:3 8.9832e-03 9.6590e-02 0.0930 0.925901 DefaultH:1 3.7573e-01 1.3608e-01 2.7612 0.005760 ** DefaultH:3 7.7333e-02 1.6206e-01 0.4772 0.633226 DefaultL:1 -5.2027e-01 1.4854e-01 -3.5025 0.000461 *** DefaultL:3 1.0127e+00 1.4445e-01 7.0107 2.371e-12 *** Labeling:1 -7.1325e-02 1.1560e-01 -0.6170 0.537248 Labeling:3 3.9963e-01 1.4548e-01 2.7470 0.006014 ** Labeling:1 2.0833e-01 1.3020e-01 1.6001 0.109578 Labeling:3 1.0587e-01 1.2573e-01 0.8420 0.399769 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Log-Likelihood: -2461.2 McFadden R^2: 0.059113 Likelihood ratio test : chisq = 309.26 (p.value = < 2.22e-16) > scoretest(m1, m2) score test data: Emission_Cat ~ 1 - 1 | Case_ID + Restaurant + Labeling + DefaultH + DefaultL + Labeling:DefaultH + Labeling:DefaultL chisq = 19.599, df = 4, p-value = 0.0005992 alternative hypothesis: unconstrained model > > #Obtaining effect sizes for labeling under high-emission-, low-emission-, and no-default conditions > DcN <- dfidx(DL, shape="wide", choice="Emission_Cat", idx="Choice_ID", subset = Default == 0) > m2N <- mlogit(Emission_Cat ~ 0|Case_ID + Restaurant + Labeling, DcN, reflevel = "2") > effects(m2N, covariate = "Labeling") 2 1 3 0.03979294 -0.06278958 0.02299665 > DcH <- dfidx(DL, shape="wide", choice="Emission_Cat", idx="Choice_ID", subset = Default == 1) > m2H <- mlogit(Emission_Cat ~ 0|Case_ID + Restaurant + Labeling, DcH, reflevel = "2") > effects(m2H, covariate = "Labeling") 2 1 3 0.02413059 -0.12116360 0.09703301 > DcL <- dfidx(DL, shape="wide", choice="Emission_Cat", idx="Choice_ID", subset = Default == 2) > m2L <- mlogit(Emission_Cat ~ 0|Case_ID + Restaurant + Labeling, DcL, reflevel = "2") > effects(m2L, covariate = "Labeling") 2 1 3 -0.01516533 -0.01869779 0.03386311 > > #Adding gender (male vs. female/diverse) and past meat-eating behavior as covariates > m3 <- mlogit(Emission_Cat ~ 0|Case_ID + Restaurant + Labeling*(DefaultH + DefaultL) + GenderM + Eat_Meat, Dc, reflevel = "2") > summary(m3) Call: mlogit(formula = Emission_Cat ~ 0 | Case_ID + Restaurant + Labeling * (DefaultH + DefaultL) + GenderM + Eat_Meat, data = Dc, reflevel = "2", method = "nr") Frequencies of alternatives:choice 2 1 3 0.34465 0.35010 0.30524 nr method 5 iterations, 0h:0m:0s g'(-H)^-1g = 0.000284 successive function values within tolerance limits Coefficients : Estimate Std. Error z-value Pr(>|z|) (Intercept):1 -1.3026e+00 2.4898e-01 -5.2318 1.678e-07 *** (Intercept):3 6.3088e-01 2.1473e-01 2.9380 0.003304 ** Case_ID:1 -7.4856e-06 1.0079e-04 -0.0743 0.940797 Case_ID:3 6.8668e-05 1.0822e-04 0.6345 0.525747 Restaurant:1 -5.4510e-03 2.4323e-02 -0.2241 0.822675 Restaurant:3 4.2180e-03 2.4577e-02 0.1716 0.863730 Labeling:1 -2.4199e-01 8.2136e-02 -2.9463 0.003216 ** Labeling:3 -1.4931e-01 1.0118e-01 -1.4756 0.140043 DefaultH:1 3.9550e-01 1.3833e-01 2.8591 0.004248 ** DefaultH:3 7.9693e-02 1.6724e-01 0.4765 0.633710 DefaultL:1 -6.3005e-01 1.5148e-01 -4.1592 3.193e-05 *** DefaultL:3 1.1626e+00 1.5104e-01 7.6976 1.377e-14 *** GenderM:1 5.0662e-01 1.2756e-01 3.9716 7.138e-05 *** GenderM:3 -2.5719e-01 1.5672e-01 -1.6411 0.100769 Eat_Meat:1 3.2909e-01 5.0689e-02 6.4923 8.455e-11 *** Eat_Meat:3 -4.1678e-01 4.0837e-02 -10.2060 < 2.2e-16 *** Labeling:1 -1.0597e-01 1.1764e-01 -0.9008 0.367705 Labeling:3 4.6937e-01 1.5016e-01 3.1258 0.001773 ** Labeling:1 1.8497e-01 1.3216e-01 1.3996 0.161635 Labeling:3 1.5361e-01 1.3020e-01 1.1799 0.238056 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Log-Likelihood: -2294.1 McFadden R^2: 0.12301 Likelihood ratio test : chisq = 643.56 (p.value = < 2.22e-16) > scoretest(m2, m3) score test data: Emission_Cat ~ 1 - 1 | Case_ID + Restaurant + Labeling + DefaultH + DefaultL + GenderM + Eat_Meat + Labeling:DefaultH + Labeling:DefaultL chisq = 455.4, df = 4, p-value < 2.2e-16 alternative hypothesis: unconstrained model > #Part 3: Linear-mixed models for GHG emissions > > library(readxl) > library(lme4) > library(MuMIn) > library(lmerTest) > > packageVersion("lme4") [1] ‘1.1.27.1’ > packageVersion("MuMIn") [1] ‘1.43.17’ > packageVersion("lmerTest") [1] ‘3.1.3’ > #Define contrasts > #We defined labeling and default contrasts so that positive values were associated with menu versions that should promote pro-environmental behavior and reduce GHG emissions (i.e., presence of values, low-emission defaults). > #The Gender1 contrast assigned -1 to male and 1 to female participants. The Gender2 contrast involved the responses from non-binary participants; these were not interpreted because there was only one. > DL$Labeling <- as.factor(DL$Labeling) > DL$Default <- as.factor(DL$Default) > DL$Gender <- as.factor(DL$Gender) > contrasts(DL$Labeling) <- cbind(c(-1,1)) > contrasts(DL$Default) <- cbind(c(-1,0,1), c(0,-1,1)) > contrasts(DL$Gender) <- cbind(c(-1,1,0), c(-1,0,1)) > > #LMM included CO2e emission of chosen dishes as DV, labeling and default contrasts as IVs. As covariates, we included the frequency of eating meat, gender, and the interaction of gender with the IVs. > > #IVs only > CO2e_pure <- lmer(Emission_kgCO2e~Labeling*Default+(1|Case_ID)+(1|Restaurant),data=DL) > r.squaredGLMM(CO2e_pure) R2m R2c [1,] 0.09692558 0.4282717 > summary(CO2e_pure) Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest'] Formula: Emission_kgCO2e ~ Labeling * Default + (1 | Case_ID) + (1 | Restaurant) Data: DL REML criterion at convergence: 4705.7 Scaled residuals: Min 1Q Median 3Q Max -2.9996 -0.6943 -0.0417 0.6674 2.8375 Random effects: Groups Name Variance Std.Dev. Case_ID (Intercept) 0.08964 0.2994 Restaurant (Intercept) 0.11899 0.3450 Residual 0.35999 0.6000 Number of obs: 2385, groups: Case_ID, 265; Restaurant, 9 Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 1.33668 0.11710 7.35927 11.415 6.06e-06 *** Labeling1 -0.10004 0.02214 262.65309 -4.519 9.41e-06 *** Default1 -0.02858 0.16354 7.00026 -0.175 0.8662 Default2 -0.25054 0.08326 7.52415 -3.009 0.0181 * Labeling1:Default1 -0.02584 0.01739 2108.76199 -1.486 0.1374 Labeling1:Default2 0.10481 0.01793 2211.07953 5.845 5.81e-09 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Correlation of Fixed Effects: (Intr) Lblng1 Deflt1 Deflt2 Lb1:D1 Labeling1 -0.008 Default1 0.000 0.000 Default2 0.000 0.002 -0.982 Lblng1:Dfl1 0.000 0.000 -0.004 0.007 Lblng1:Dfl2 0.002 -0.003 0.003 -0.012 -0.489 > > #IVs + Covs > CO2e_wcov <- lmer(Emission_kgCO2e~Labeling*Default*Gender+Eat_Meat+(1|Case_ID)+(1|Restaurant),data=DL) fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients > anova(CO2e_pure,CO2e_wcov) refitting model(s) with ML (instead of REML) Data: DL Models: CO2e_pure: Emission_kgCO2e ~ Labeling * Default + (1 | Case_ID) + (1 | Restaurant) CO2e_wcov: Emission_kgCO2e ~ Labeling * Default * Gender + Eat_Meat + (1 | Case_ID) + (1 | Restaurant) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) CO2e_pure 9 4694.2 4746.2 -2338.1 4676.2 CO2e_wcov 19 4570.3 4680.0 -2266.1 4532.3 143.91 10 < 2.2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > r.squaredGLMM(CO2e_wcov) R2m R2c [1,] 0.1772583 0.4277267 > summary(CO2e_wcov) Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest'] Formula: Emission_kgCO2e ~ Labeling * Default * Gender + Eat_Meat + (1 | Case_ID) + (1 | Restaurant) Data: DL REML criterion at convergence: 4609 Scaled residuals: Min 1Q Median 3Q Max -2.99227 -0.70078 -0.02063 0.72267 2.91969 Random effects: Groups Name Variance Std.Dev. Case_ID (Intercept) 0.03851 0.1963 Restaurant (Intercept) 0.11894 0.3449 Residual 0.35976 0.5998 Number of obs: 2385, groups: Case_ID, 265; Restaurant, 9 Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 9.261e-01 1.571e-01 2.339e+01 5.895 4.88e-06 *** Labeling1 -5.704e-02 2.225e-02 2.609e+02 -2.563 0.0109 * Default1 1.378e-01 1.887e-01 1.241e+01 0.730 0.4787 Default2 -2.323e-01 1.257e-01 3.893e+01 -1.848 0.0722 . Gender1 -1.260e-01 9.569e-02 2.583e+02 -1.317 0.1891 Gender2 3.467e-02 1.880e-01 2.584e+02 0.184 0.8538 Eat_Meat 1.425e-01 1.313e-02 2.588e+02 10.851 < 2e-16 *** Labeling1:Default1 -1.360e-02 2.245e-02 2.104e+03 -0.606 0.5447 Labeling1:Default2 1.199e-01 2.350e-02 2.255e+03 5.103 3.63e-07 *** Labeling1:Gender1 -1.612e-02 2.252e-02 2.611e+02 -0.716 0.4746 Default1:Gender1 -1.641e-01 9.641e-02 2.103e+03 -1.702 0.0889 . Default2:Gender1 -2.605e-02 9.663e-02 2.110e+03 -0.270 0.7875 Default1:Gender2 3.497e-01 1.897e-01 2.103e+03 1.844 0.0654 . Default2:Gender2 -3.344e-03 1.902e-01 2.106e+03 -0.018 0.9860 Labeling1:Default1:Gender1 -1.750e-02 2.245e-02 2.104e+03 -0.779 0.4359 Labeling1:Default2:Gender1 -2.085e-02 2.351e-02 2.256e+03 -0.887 0.3754 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Correlation matrix not shown by default, as p = 16 > 12. Use print(x, correlation=TRUE) or vcov(x) if you need it fit warnings: fixed-effect model matrix is rank deficient so dropping 3 columns / coefficients