m_school_r_2 <- lmer(
s_diversion ~ game_time_num_c_2 + attendance_school_z+ game_result + s_game_c + area_classification + tenure_year_c + total_revenues_z +conference + (1+tenure_year_c|school),
data = data_clean, control = lmerControl(optimizer = "bobyqa"), REML = FALSE
)Waste Management Project Update (Part IV - tentative model comparison)
This document aims to provide an informal comparison of three models that have been fitted in the [Title name : Two level (game-school) models with fixed effect and random effect predictors].
Since these three models have different fixed predictors (and different random effects), we use the maximum likelihood method (REML=FALSE) in lmer function, not the Restricted Maximum Likelihood (REML=TRUE).
1. Summary Outputs
1.1 Two level (game-school) model with main effects
summary(m_school_r_2)Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
method [lmerModLmerTest]
Formula: s_diversion ~ game_time_num_c_2 + attendance_school_z + game_result +
s_game_c + area_classification + tenure_year_c + total_revenues_z +
conference + (1 + tenure_year_c | school)
Data: data_clean
Control: lmerControl(optimizer = "bobyqa")
AIC BIC logLik -2*log(L) df.resid
-1723.3 -1641.2 877.6 -1755.3 1229
Scaled residuals:
Min 1Q Median 3Q Max
-4.3719 -0.5641 -0.0701 0.4776 3.9566
Random effects:
Groups Name Variance Std.Dev. Corr
school (Intercept) 0.04541 0.21310
tenure_year_c 0.00111 0.03332 -0.22
Residual 0.01216 0.11028
Number of obs: 1245, groups: school, 27
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 5.215e-01 1.732e-01 2.684e+01 3.011 0.00562 **
game_time_num_c_2 -3.686e-04 1.148e-03 1.201e+03 -0.321 0.74812
attendance_school_z 2.722e-03 3.409e-03 1.215e+03 0.799 0.42468
game_result1 8.229e-03 7.577e-03 1.201e+03 1.086 0.27766
s_game_c -5.663e-04 1.633e-03 1.196e+03 -0.347 0.72887
area_classification1 -7.463e-02 1.372e-01 2.658e+01 -0.544 0.59090
tenure_year_c 7.392e-03 7.248e-03 2.610e+01 1.020 0.31713
total_revenues_z 2.391e-02 9.218e-03 1.230e+03 2.593 0.00962 **
conferenceBig10 -1.400e-01 1.267e-01 2.607e+01 -1.105 0.27922
conferenceBig12 -2.593e-01 1.819e-01 2.654e+01 -1.426 0.16566
conferencePac12 2.111e-03 1.572e-01 2.918e+01 0.013 0.98937
conferenceSEC -2.309e-01 1.314e-01 2.624e+01 -1.758 0.09044 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) g____2 attn__ gm_rs1 s_gm_c ar_cl1 tnr_y_ ttl_r_ cnfB10
gm_tm_nm__2 -0.024
attndnc_sc_ -0.012 -0.116
game_reslt1 -0.036 0.040 0.097
s_game_c -0.036 0.148 -0.046 0.169
ar_clssfct1 -0.792 0.001 0.002 -0.002 0.000
tenure_yr_c -0.060 -0.014 0.050 -0.019 0.007 -0.012
totl_rvns_z 0.074 -0.004 -0.087 -0.036 -0.032 -0.020 -0.184
confrncBg10 -0.672 0.005 0.011 0.006 0.002 0.218 0.009 -0.047
confrncBg12 -0.350 -0.005 0.013 0.005 0.007 0.001 0.008 -0.050 0.475
confrncPc12 -0.592 -0.009 0.005 0.020 0.004 0.246 -0.047 0.014 0.600
conferncSEC -0.484 -0.009 0.006 0.003 -0.001 0.001 0.022 -0.058 0.657
cnfB12 cnfP12
gm_tm_nm__2
attndnc_sc_
game_reslt1
s_game_c
ar_clssfct1
tenure_yr_c
totl_rvns_z
confrncBg10
confrncBg12
confrncPc12 0.381
conferncSEC 0.459 0.5271.2 Two level (game-school) model with interaction effects
m_school_inter_r_2 <- lmer(
s_diversion ~ 1 + game_time_num_c_2 + s_game_c + area_classification + attendance_school_z + game_result + tenure_year_c
+ total_revenues_z
+ conference
+ total_revenues_z:tenure_year_c
+ attendance_school_z:tenure_year_c
+ game_result:tenure_year_c
+ area_classification:total_revenues_z
+ (1 + tenure_year_c | school),
data = data_clean,
control = lmerControl(optimizer = "bobyqa"), REML = FALSE
)summary(m_school_inter_r_2)Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
method [lmerModLmerTest]
Formula:
s_diversion ~ 1 + game_time_num_c_2 + s_game_c + area_classification +
attendance_school_z + game_result + tenure_year_c + total_revenues_z +
conference + total_revenues_z:tenure_year_c + attendance_school_z:tenure_year_c +
game_result:tenure_year_c + area_classification:total_revenues_z +
(1 + tenure_year_c | school)
Data: data_clean
Control: lmerControl(optimizer = "bobyqa")
AIC BIC logLik -2*log(L) df.resid
-1760.7 -1658.2 900.4 -1800.7 1225
Scaled residuals:
Min 1Q Median 3Q Max
-4.4269 -0.5159 -0.0567 0.4811 3.8762
Random effects:
Groups Name Variance Std.Dev. Corr
school (Intercept) 0.042894 0.20711
tenure_year_c 0.001005 0.03171 -0.17
Residual 0.011739 0.10834
Number of obs: 1245, groups: school, 27
Fixed effects:
Estimate Std. Error df t value
(Intercept) 7.736e-01 1.844e-01 3.539e+01 4.195
game_time_num_c_2 -3.441e-04 1.132e-03 1.203e+03 -0.304
s_game_c -7.876e-04 1.606e-03 1.196e+03 -0.491
area_classification1 -2.500e-01 1.513e-01 3.633e+01 -1.652
attendance_school_z -9.838e-03 5.383e-03 1.220e+03 -1.828
game_result1 -9.352e-03 1.110e-02 1.206e+03 -0.843
tenure_year_c -5.397e-03 7.259e-03 3.105e+01 -0.744
total_revenues_z 2.829e-01 8.262e-02 2.180e+02 3.424
conferenceBig10 -1.813e-01 1.249e-01 2.636e+01 -1.452
conferenceBig12 -3.537e-01 1.798e-01 2.712e+01 -1.968
conferencePac12 1.251e-03 1.549e-01 2.952e+01 0.008
conferenceSEC -2.749e-01 1.294e-01 2.647e+01 -2.125
tenure_year_c:total_revenues_z -6.155e-03 1.124e-03 1.231e+03 -5.474
attendance_school_z:tenure_year_c 1.508e-03 5.863e-04 1.212e+03 2.572
game_result1:tenure_year_c 2.973e-03 1.713e-03 1.208e+03 1.735
area_classification1:total_revenues_z -1.859e-01 8.286e-02 2.156e+02 -2.243
Pr(>|t|)
(Intercept) 0.000174 ***
game_time_num_c_2 0.761122
s_game_c 0.623864
area_classification1 0.107152
attendance_school_z 0.067857 .
game_result1 0.399620
tenure_year_c 0.462764
total_revenues_z 0.000738 ***
conferenceBig10 0.158250
conferenceBig12 0.059388 .
conferencePac12 0.993611
conferenceSEC 0.043060 *
tenure_year_c:total_revenues_z 5.33e-08 ***
attendance_school_z:tenure_year_c 0.010243 *
game_result1:tenure_year_c 0.082982 .
area_classification1:total_revenues_z 0.025903 *
---
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 it1.3 Two level (game-school) models with interaction and nonlinear effects
m_school_polytenure_inter_r_2 <- lmer(
s_diversion ~ 1 + game_time_num_c_2 + attendance_school_z + game_result + s_game_c + conference + area_classification
+ total_revenues_z
+ poly(tenure_year_c , 3)
+ poly(tenure_year_c , 3):conference
+ poly(tenure_year_c , 3):attendance_school_z
+ area_classification:total_revenues_z
+ poly(tenure_year_c , 3):total_revenues_z
+ (1 + poly(tenure_year_c , 2) | school),
data = data_clean,
control = lmerControl(optimizer = "bobyqa"), REML = FALSE
)summary(m_school_polytenure_inter_r_2)Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
method [lmerModLmerTest]
Formula:
s_diversion ~ 1 + game_time_num_c_2 + attendance_school_z + game_result +
s_game_c + conference + area_classification + total_revenues_z +
poly(tenure_year_c, 3) + poly(tenure_year_c, 3):conference +
poly(tenure_year_c, 3):attendance_school_z + area_classification:total_revenues_z +
poly(tenure_year_c, 3):total_revenues_z + (1 + poly(tenure_year_c,
2) | school)
Data: data_clean
Control: lmerControl(optimizer = "bobyqa")
AIC BIC logLik -2*log(L) df.resid
-1961.3 -1756.2 1020.6 -2041.3 1205
Scaled residuals:
Min 1Q Median 3Q Max
-4.8097 -0.5172 -0.0286 0.4532 4.4720
Random effects:
Groups Name Variance Std.Dev. Corr
school (Intercept) 6.097e-02 0.24692
poly(tenure_year_c, 2)1 1.057e+02 10.28145 0.57
poly(tenure_year_c, 2)2 1.310e+01 3.61876 0.39 0.88
Residual 9.383e-03 0.09687
Number of obs: 1245, groups: school, 27
Fixed effects:
Estimate Std. Error df
(Intercept) 6.737e-01 2.159e-01 2.803e+01
game_time_num_c_2 -9.005e-05 1.017e-03 1.184e+03
attendance_school_z -1.734e-03 3.361e-03 1.212e+03
game_result1 5.003e-03 6.765e-03 1.188e+03
s_game_c 2.993e-05 1.439e-03 1.169e+03
conferenceBig10 -3.848e-03 1.796e-01 1.547e+01
conferenceBig12 -1.962e-01 2.594e-01 1.571e+01
conferencePac12 1.266e-01 2.114e-01 1.661e+01
conferenceSEC -3.277e-01 1.952e-01 1.589e+01
area_classification1 -3.492e-01 1.521e-01 3.638e+01
total_revenues_z 4.056e-01 1.001e-01 9.128e+01
poly(tenure_year_c, 3)1 -9.395e+00 7.736e+00 7.778e+00
poly(tenure_year_c, 3)2 -2.272e+00 3.176e+00 5.890e+00
poly(tenure_year_c, 3)3 2.945e+00 7.128e-01 3.184e+02
conferenceBig10:poly(tenure_year_c, 3)1 7.360e+00 8.844e+00 7.722e+00
conferenceBig12:poly(tenure_year_c, 3)1 5.159e+00 1.239e+01 6.860e+00
conferencePac12:poly(tenure_year_c, 3)1 8.745e+00 1.026e+01 7.512e+00
conferenceSEC:poly(tenure_year_c, 3)1 -8.876e+00 9.985e+00 8.505e+00
conferenceBig10:poly(tenure_year_c, 3)2 5.915e-01 3.631e+00 6.044e+00
conferenceBig12:poly(tenure_year_c, 3)2 -3.167e+00 5.228e+00 6.674e+00
conferencePac12:poly(tenure_year_c, 3)2 2.553e+00 4.233e+00 6.104e+00
conferenceSEC:poly(tenure_year_c, 3)2 -1.169e+01 4.337e+00 7.261e+00
conferenceBig10:poly(tenure_year_c, 3)3 -4.641e+00 8.505e-01 3.448e+02
conferenceBig12:poly(tenure_year_c, 3)3 -5.558e+00 1.934e+00 1.002e+02
conferencePac12:poly(tenure_year_c, 3)3 -5.284e+00 1.193e+00 1.427e+02
conferenceSEC:poly(tenure_year_c, 3)3 -8.804e+00 1.067e+00 2.712e+02
attendance_school_z:poly(tenure_year_c, 3)1 2.944e-01 1.019e-01 1.205e+03
attendance_school_z:poly(tenure_year_c, 3)2 -7.283e-02 1.014e-01 1.214e+03
attendance_school_z:poly(tenure_year_c, 3)3 -2.621e-01 1.098e-01 1.207e+03
area_classification1:total_revenues_z -3.502e-01 1.010e-01 9.412e+01
total_revenues_z:poly(tenure_year_c, 3)1 -6.727e-01 3.158e-01 1.023e+03
total_revenues_z:poly(tenure_year_c, 3)2 6.526e-01 3.546e-01 5.187e+02
total_revenues_z:poly(tenure_year_c, 3)3 -4.520e-01 1.962e-01 4.782e+02
t value Pr(>|t|)
(Intercept) 3.120 0.004162 **
game_time_num_c_2 -0.089 0.929432
attendance_school_z -0.516 0.606032
game_result1 0.740 0.459698
s_game_c 0.021 0.983414
conferenceBig10 -0.021 0.983183
conferenceBig12 -0.756 0.460747
conferencePac12 0.599 0.557238
conferenceSEC -1.679 0.112782
area_classification1 -2.295 0.027586 *
total_revenues_z 4.053 0.000106 ***
poly(tenure_year_c, 3)1 -1.214 0.260153
poly(tenure_year_c, 3)2 -0.715 0.501835
poly(tenure_year_c, 3)3 4.131 4.62e-05 ***
conferenceBig10:poly(tenure_year_c, 3)1 0.832 0.430274
conferenceBig12:poly(tenure_year_c, 3)1 0.416 0.689892
conferencePac12:poly(tenure_year_c, 3)1 0.852 0.420602
conferenceSEC:poly(tenure_year_c, 3)1 -0.889 0.398487
conferenceBig10:poly(tenure_year_c, 3)2 0.163 0.875898
conferenceBig12:poly(tenure_year_c, 3)2 -0.606 0.564628
conferencePac12:poly(tenure_year_c, 3)2 0.603 0.568158
conferenceSEC:poly(tenure_year_c, 3)2 -2.697 0.029748 *
conferenceBig10:poly(tenure_year_c, 3)3 -5.457 9.27e-08 ***
conferenceBig12:poly(tenure_year_c, 3)3 -2.875 0.004942 **
conferencePac12:poly(tenure_year_c, 3)3 -4.429 1.87e-05 ***
conferenceSEC:poly(tenure_year_c, 3)3 -8.249 6.96e-15 ***
attendance_school_z:poly(tenure_year_c, 3)1 2.888 0.003943 **
attendance_school_z:poly(tenure_year_c, 3)2 -0.718 0.472839
attendance_school_z:poly(tenure_year_c, 3)3 -2.387 0.017153 *
area_classification1:total_revenues_z -3.469 0.000790 ***
total_revenues_z:poly(tenure_year_c, 3)1 -2.130 0.033384 *
total_revenues_z:poly(tenure_year_c, 3)2 1.840 0.066275 .
total_revenues_z:poly(tenure_year_c, 3)3 -2.304 0.021634 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation matrix not shown by default, as p = 33 > 12.
Use print(x, correlation=TRUE) or
vcov(x) if you need it2. Model Performance
performance::model_performance(m_school_r_2,estimator = "ML")# Indices of model performance
AIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma
-----------------------------------------------------------------------------
-1723.3 | -1722.8 | -1641.2 | 0.885 | 0.086 | 0.875 | 0.108 | 0.110performance::model_performance(m_school_inter_r_2,estimator = "ML")# Indices of model performance
AIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma
-----------------------------------------------------------------------------
-1760.7 | -1760.0 | -1658.2 | 0.887 | 0.100 | 0.875 | 0.106 | 0.108performance::model_performance(m_school_polytenure_inter_r_2,estimator = "ML")# Indices of model performance
AIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma
-----------------------------------------------------------------------------
-1961.3 | -1958.6 | -1756.2 | 0.908 | 0.312 | 0.867 | 0.095 | 0.097