Co2 Growth Model
Miles Yang, Yucheng Zhang, Lei Lei, Dayong Zhang and Peter Li
2 EXPLORATORY DESCRIPTION
## Descriptive Statistics:
## ─────────────────────────────────────────────────────────────────────────────────────────────────────────
## N (NA) Mean SD | Median Min Max Skewness Kurtosis
## ─────────────────────────────────────────────────────────────────────────────────────────────────────────
## firm* 6034 791.61 445.70 | 765.00 1.00 1601.00 0.08 -1.06
## fiscal_year 6034 2019.35 2.50 | 2020.00 2014.00 2022.00 -0.79 -0.66
## carbon_emission_scope1 5959 75 2451641.45 9526167.65 | 49700.00 0.00 144000000.00 7.15 64.51
## carbon_emission_scope2 5811 223 590156.10 2464980.72 | 76900.00 0.00 64171000.00 14.88 301.77
## W* 6034 1.72 0.45 | 2.00 1.00 2.00 -1.01 -0.99
## T 6034 1.72 1.06 | 2.00 0.00 3.00 -0.25 -1.19
## Y1 5959 75 2.45 9.53 | 0.05 0.00 144.00 7.15 64.51
## Y2 5811 223 0.59 2.46 | 0.08 0.00 64.17 14.88 301.77
## Clus* 6034 1041.70 597.90 | 1016.00 1.00 2110.00 0.05 -1.13
## ─────────────────────────────────────────────────────────────────────────────────────────────────────────
##
## NOTE: `firm`, `W`, `Clus` transformed to numeric.
3 LINEAR GROWTH MODEL FOR CARBON EMISSIONS (Scope 1)
3.1 Intraclass correlation estimates
##
## Hierarchical Linear Model (HLM)
## (also known as) Linear Mixed Model (LMM)
## (also known as) Multilevel Linear Model (MLM)
##
## Model Information:
## Formula: Y1 ~ 1 + (1 | Clus)
## Level-1 Observations: N = 5959
## Level-2 Groups/Clusters: Clus, 2082
##
## Model Fit:
## AIC = 30271.033
## BIC = 30291.111
## R_(m)² = 0.00000 (Marginal R²: fixed effects)
## R_(c)² = 0.97726 (Conditional R²: fixed + random effects)
## Omega² = NA (= 1 - proportion of unexplained variance)
##
## Fixed Effects:
## Unstandardized Coefficients (b or γ):
## Outcome Variable: Y1
## ─────────────────────────────────────────────────────────────────
## b/γ S.E. t df p [95% CI of b/γ]
## ─────────────────────────────────────────────────────────────────
## (Intercept) 2.076 (0.194) 10.68 2086.1 <.001 *** [1.695, 2.457]
## ─────────────────────────────────────────────────────────────────
## 'df' is estimated by Satterthwaite approximation.
##
## Random Effects:
## ───────────────────────────────────────────
## Cluster K Parameter Variance ICC
## ───────────────────────────────────────────
## Clus 2082 (Intercept) 77.82534 0.97726
## Residual 1.81124
## ───────────────────────────────────────────##
## ------ Sample Size Information ------
##
## Level 1: N = 5959 observations ("Y1")
## Level 2: K = 2082 groups ("Clus")
##
## n (group sizes)
## Min. 1.000
## Median 3.000
## Mean 2.862
## Max. 4.000
##
## ------ ICC(1), ICC(2), and rWG ------
##
## ICC variable: "Y1"
##
## ICC(1) = 0.977 (non-independence of data)
## ICC(2) = 0.990 (reliability of group means)
##
## rWG variable: "Y1"
##
## rWG (within-group agreement for single-item measures)
## ─────────────────────────────────────────────────────
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## ─────────────────────────────────────────────────────
## rWG 0.709 1.000 1.000 0.999 1.000 1.000 383.000
## ─────────────────────────────────────────────────────3.2 Unconditional growth model: 1-1
##
## Hierarchical Linear Model (HLM)
## (also known as) Linear Mixed Model (LMM)
## (also known as) Multilevel Linear Model (MLM)
##
## Model Information:
## Formula: Y1 ~ T + (T | Clus)
## Level-1 Observations: N = 5959
## Level-2 Groups/Clusters: Clus, 2082
##
## Model Fit:
## AIC = 28798.241
## BIC = 28838.397
## R_(m)² = 0.00005 (Marginal R²: fixed effects)
## R_(c)² = 0.98929 (Conditional R²: fixed + random effects)
## Omega² = NA (= 1 - proportion of unexplained variance)
##
## ANOVA Table:
## ──────────────────────────────────────────────
## Sum Sq Mean Sq NumDF DenDF F p
## ──────────────────────────────────────────────
## T 5.95 5.95 1.00 1968.02 6.93 .009 **
## ──────────────────────────────────────────────
##
## Fixed Effects:
## Unstandardized Coefficients (b or γ):
## Outcome Variable: Y1
## ───────────────────────────────────────────────────────────────────
## b/γ S.E. t df p [95% CI of b/γ]
## ───────────────────────────────────────────────────────────────────
## (Intercept) 2.172 (0.213) 10.18 2096.0 <.001 *** [ 1.754, 2.590]
## T -0.060 (0.023) -2.63 1968.0 .009 ** [-0.104, -0.015]
## ───────────────────────────────────────────────────────────────────
## 'df' is estimated by Satterthwaite approximation.
##
## Standardized Coefficients (β):
## Outcome Variable: Y1
## ─────────────────────────────────────────────────────────
## β S.E. t df p [95% CI of β]
## ─────────────────────────────────────────────────────────
## T -0.007 (0.003) -2.63 1968.0 .009 ** [-0.012, -0.002]
## ─────────────────────────────────────────────────────────
##
## Random Effects:
## ───────────────────────────────────────────
## Cluster K Parameter Variance ICC
## ───────────────────────────────────────────
## Clus 2082 (Intercept) 91.94705 0.99075
## T 0.54333
## Residual 0.85865
## ───────────────────────────────────────────3.3 Conditional growth model: Build the Level 2 Model
##
## Hierarchical Linear Model (HLM)
## (also known as) Linear Mixed Model (LMM)
## (also known as) Multilevel Linear Model (MLM)
##
## Model Information:
## Formula: Y1 ~ T + W + (T | Clus)
## Level-1 Observations: N = 5959
## Level-2 Groups/Clusters: Clus, 2082
##
## Model Fit:
## AIC = 28788.152
## BIC = 28835.001
## R_(m)² = 0.00506 (Marginal R²: fixed effects)
## R_(c)² = 0.98923 (Conditional R²: fixed + random effects)
## Omega² = NA (= 1 - proportion of unexplained variance)
##
## ANOVA Table:
## ───────────────────────────────────────────────
## Sum Sq Mean Sq NumDF DenDF F p
## ───────────────────────────────────────────────
## T 6.08 6.08 1.00 1965.27 7.08 .008 **
## W 10.49 10.49 1.00 2147.59 12.22 <.001 ***
## ───────────────────────────────────────────────
##
## Fixed Effects:
## Unstandardized Coefficients (b or γ):
## Outcome Variable: Y1
## ───────────────────────────────────────────────────────────────────
## b/γ S.E. t df p [95% CI of b/γ]
## ───────────────────────────────────────────────────────────────────
## (Intercept) 3.204 (0.364) 8.81 2410.8 <.001 *** [ 2.491, 3.917]
## T -0.060 (0.023) -2.66 1965.3 .008 ** [-0.105, -0.016]
## W1 -1.412 (0.404) -3.50 2147.6 <.001 *** [-2.204, -0.620]
## ───────────────────────────────────────────────────────────────────
## 'df' is estimated by Satterthwaite approximation.
##
## Standardized Coefficients (β):
## Outcome Variable: Y1
## ──────────────────────────────────────────────────────────
## β S.E. t df p [95% CI of β]
## ──────────────────────────────────────────────────────────
## T -0.007 (0.003) -2.66 1965.3 .008 ** [-0.012, -0.002]
## W1 -0.066 (0.019) -3.50 2147.6 <.001 *** [-0.103, -0.029]
## ──────────────────────────────────────────────────────────
##
## Random Effects:
## ───────────────────────────────────────────
## Cluster K Parameter Variance ICC
## ───────────────────────────────────────────
## Clus 2082 (Intercept) 90.95343 0.99064
## T 0.54326
## Residual 0.85901
## ───────────────────────────────────────────3.4 Running a 1×2 model with grandmean-centered W
##
## ****************** PART 1. Regression Model Summary ******************
##
## PROCESS Model Code : 1 (Hayes, 2018; www.guilford.com/p/hayes3)
## PROCESS Model Type : Simple Moderation
## - Outcome (Y) : Y1
## - Predictor (X) : T
## - Mediators (M) : -
## - Moderators (W) : W
## - Covariates (C) : -
## - HLM Clusters : Clus
##
## Formula of Outcome:
## - Y1 ~ T*W + (T|Clus)
##
## CAUTION:
## Fixed effect (coef.) of a predictor involved in an interaction
## denotes its "simple effect/slope" at the other predictor = 0.
## Only when all predictors in an interaction are mean-centered
## can the fixed effect denote the "main effect"!
##
## Model Summary
##
## ─────────────────────────────────────────────────────
## (1) Y1 (2) Y1
## ─────────────────────────────────────────────────────
## (Intercept) 2.172 *** 4.034 ***
## (0.213) (0.408)
## T -0.060 ** -0.225 ***
## (0.023) (0.043)
## W1 -2.553 ***
## (0.477)
## T:W1 0.227 ***
## (0.050)
## ─────────────────────────────────────────────────────
## Marginal R^2 0.000 0.012
## Conditional R^2 0.989 0.989
## AIC 28798.241 28774.157
## BIC 28838.397 28827.698
## Num. obs. 5959 5959
## Num. groups: Clus 2082 2082
## Var: Clus (Intercept) 91.947 90.760
## Var: Clus T 0.543 0.535
## Cov: Clus (Intercept) T -4.320 -4.219
## Var: Residual 0.859 0.858
## ─────────────────────────────────────────────────────
## Note. * p < .05, ** p < .01, *** p < .001.
##
## ************ PART 2. Mediation/Moderation Effect Estimate ************
##
## Package Use : ‘interactions’ (v1.1.5)
## Effect Type : Simple Moderation (Model 1)
## Sample Size : 5959 (75 missing observations deleted)
## Random Seed : -
## Simulations : -
##
## Interaction Effect on "Y1" (Y)
## ───────────────────────────────
## F df1 df2 p
## ───────────────────────────────
## T * W 20.25 1 1896 <.001 ***
## ───────────────────────────────
##
## Simple Slopes: "T" (X) ==> "Y1" (Y)
## ─────────────────────────────────────────────────────
## "W" Effect S.E. t p [95% CI]
## ─────────────────────────────────────────────────────
## 0 -0.225 (0.043) -5.238 <.001 *** [-0.309, -0.141]
## 1 0.002 (0.027) 0.090 .929 [-0.050, 0.054]
## ─────────────────────────────────────────────────────Interpretation of cross level results of growth model:
The intercept γ00=54.704: The predicted Y who are at the T= 0 and W = 0.
γ10 of T=-5.143: There is a significant main effect of time. Specifically, Y changes by -5.143 day for an observation that is at the W =0.
γ10 of W=-.425: There is a insignificant main effect of W, such that the expectation that observation that is higher in W are less Y at T = 0 than observations who are lower in W is not supported.
γ11 of T*W=.064: The change in the growth rate (slope of T on Y) across Clus when W increases by 1 point.
Simple slope tests (e.g., Preacher, Curran, & Bauer, 2006): This test is used to examine growth rate (i.e., relationship between T and Y) is significant at a particular value of W. T was significantly related to Y for both High-W and Low-W types. The simple slope for growth rate (slope of T on Y) is negative in Low-W group (γ = -4.061, p < .001), whereas the growth rate less negative in Low-W group (γ = −1.191, p < .05).
But since the raw value is used, it should be interpreted. The problem is that W does not have a 0 value. Therefore, it is recommended to use the value of W group centering in the analysis
3.4.1 Draw adjustment diagram
##
## Model Summary
##
## ────────────────────────────────────────────────────────────────────────────────────
## y (MLMNull) y (MLM11RR.a1) y (MLM21RR.b1) y (MLM1x2.c2)
## ────────────────────────────────────────────────────────────────────────────────────
## (Intercept) 2.08 *** 2.17 *** 3.20 *** 4.03 ***
## (0.19) (0.21) (0.36) (0.41)
## T -0.06 ** -0.06 ** -0.22 ***
## (0.02) (0.02) (0.04)
## W1 -1.41 *** -2.55 ***
## (0.40) (0.48)
## T:W1 0.23 ***
## (0.05)
## ────────────────────────────────────────────────────────────────────────────────────
## Marginal R^2 0.00 0.00 0.01 0.01
## Conditional R^2 0.98 0.99 0.99 0.99
## AIC 30271.03 28798.24 28788.15 28774.16
## BIC 30291.11 28838.40 28835.00 28827.70
## Num. obs. 5959 5959 5959 5959
## Num. groups: Clus 2082 2082 2082 2082
## Var: Clus (Intercept) 77.83 91.95 90.95 90.76
## Var: Residual 1.81 0.86 0.86 0.86
## Var: Clus T 0.54 0.54 0.53
## Cov: Clus (Intercept) T -4.32 -4.26 -4.22
## ────────────────────────────────────────────────────────────────────────────────────
## Note. * p < .05, ** p < .01, *** p < .001.4 LINEAR GROWTH MODEL FOR CARBON EMISSIONS (SCOPE 2)
4.1 Intraclass correlation estimates
##
## Hierarchical Linear Model (HLM)
## (also known as) Linear Mixed Model (LMM)
## (also known as) Multilevel Linear Model (MLM)
##
## Model Information:
## Formula: Y2 ~ 1 + (1 | Clus)
## Level-1 Observations: N = 5811
## Level-2 Groups/Clusters: Clus, 2049
##
## Model Fit:
## AIC = 21748.618
## BIC = 21768.621
## R_(m)² = 0.00000 (Marginal R²: fixed effects)
## R_(c)² = 0.82115 (Conditional R²: fixed + random effects)
## Omega² = NA (= 1 - proportion of unexplained variance)
##
## Fixed Effects:
## Unstandardized Coefficients (b or γ):
## Outcome Variable: Y2
## ─────────────────────────────────────────────────────────────────
## b/γ S.E. t df p [95% CI of b/γ]
## ─────────────────────────────────────────────────────────────────
## (Intercept) 0.526 (0.050) 10.59 2086.7 <.001 *** [0.429, 0.624]
## ─────────────────────────────────────────────────────────────────
## 'df' is estimated by Satterthwaite approximation.
##
## Random Effects:
## ───────────────────────────────────────────
## Cluster K Parameter Variance ICC
## ───────────────────────────────────────────
## Clus 2049 (Intercept) 4.61345 0.82115
## Residual 1.00480
## ───────────────────────────────────────────##
## ------ Sample Size Information ------
##
## Level 1: N = 5811 observations ("Y2")
## Level 2: K = 2049 groups ("Clus")
##
## n (group sizes)
## Min. 1.000
## Median 3.000
## Mean 2.836
## Max. 4.000
##
## ------ ICC(1), ICC(2), and rWG ------
##
## ICC variable: "Y2"
##
## ICC(1) = 0.821 (non-independence of data)
## ICC(2) = 0.912 (reliability of group means)
##
## rWG variable: "Y2"
##
## rWG (within-group agreement for single-item measures)
## ─────────────────────────────────────────────────────
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## ─────────────────────────────────────────────────────
## rWG 0.000 1.000 1.000 0.998 1.000 1.000 399.000
## ─────────────────────────────────────────────────────4.2 Unconditional growth model: 1-1
##
## Hierarchical Linear Model (HLM)
## (also known as) Linear Mixed Model (LMM)
## (also known as) Multilevel Linear Model (MLM)
##
## Model Information:
## Formula: Y2 ~ T + (T | Clus)
## Level-1 Observations: N = 5811
## Level-2 Groups/Clusters: Clus, 2049
##
## Model Fit:
## AIC = 21040.022
## BIC = 21080.027
## R_(m)² = 0.00057 (Marginal R²: fixed effects)
## R_(c)² = 0.89646 (Conditional R²: fixed + random effects)
## Omega² = NA (= 1 - proportion of unexplained variance)
##
## ANOVA Table:
## ──────────────────────────────────────────────
## Sum Sq Mean Sq NumDF DenDF F p
## ──────────────────────────────────────────────
## T 5.73 5.73 1.00 1597.51 9.48 .002 **
## ──────────────────────────────────────────────
##
## Fixed Effects:
## Unstandardized Coefficients (b or γ):
## Outcome Variable: Y2
## ───────────────────────────────────────────────────────────────────
## b/γ S.E. t df p [95% CI of b/γ]
## ───────────────────────────────────────────────────────────────────
## (Intercept) 0.623 (0.068) 9.16 1900.7 <.001 *** [ 0.490, 0.757]
## T -0.054 (0.018) -3.08 1597.5 .002 ** [-0.088, -0.020]
## ───────────────────────────────────────────────────────────────────
## 'df' is estimated by Satterthwaite approximation.
##
## Standardized Coefficients (β):
## Outcome Variable: Y2
## ─────────────────────────────────────────────────────────
## β S.E. t df p [95% CI of β]
## ─────────────────────────────────────────────────────────
## T -0.023 (0.008) -3.08 1597.5 .002 ** [-0.038, -0.008]
## ─────────────────────────────────────────────────────────
##
## Random Effects:
## ───────────────────────────────────────────
## Cluster K Parameter Variance ICC
## ───────────────────────────────────────────
## Clus 2049 (Intercept) 7.62329 0.92652
## T 0.27783
## Residual 0.60457
## ───────────────────────────────────────────4.3 Conditional growth model: Build the Level 2 Model
##
## Hierarchical Linear Model (HLM)
## (also known as) Linear Mixed Model (LMM)
## (also known as) Multilevel Linear Model (MLM)
##
## Model Information:
## Formula: Y2 ~ T + W + (T | Clus)
## Level-1 Observations: N = 5811
## Level-2 Groups/Clusters: Clus, 2049
##
## Model Fit:
## AIC = 21016.300
## BIC = 21062.973
## R_(m)² = 0.01173 (Marginal R²: fixed effects)
## R_(c)² = 0.89653 (Conditional R²: fixed + random effects)
## Omega² = NA (= 1 - proportion of unexplained variance)
##
## ANOVA Table:
## ───────────────────────────────────────────────
## Sum Sq Mean Sq NumDF DenDF F p
## ───────────────────────────────────────────────
## T 5.85 5.85 1.00 1597.29 9.68 .002 **
## W 17.26 17.26 1.00 2081.92 28.56 <.001 ***
## ───────────────────────────────────────────────
##
## Fixed Effects:
## Unstandardized Coefficients (b or γ):
## Outcome Variable: Y2
## ───────────────────────────────────────────────────────────────────
## b/γ S.E. t df p [95% CI of b/γ]
## ───────────────────────────────────────────────────────────────────
## (Intercept) 1.044 (0.104) 10.05 2707.6 <.001 *** [ 0.840, 1.247]
## T -0.055 (0.018) -3.11 1597.3 .002 ** [-0.089, -0.020]
## W1 -0.570 (0.107) -5.34 2081.9 <.001 *** [-0.779, -0.361]
## ───────────────────────────────────────────────────────────────────
## 'df' is estimated by Satterthwaite approximation.
##
## Standardized Coefficients (β):
## Outcome Variable: Y2
## ──────────────────────────────────────────────────────────
## β S.E. t df p [95% CI of β]
## ──────────────────────────────────────────────────────────
## T -0.024 (0.008) -3.11 1597.3 .002 ** [-0.038, -0.009]
## W1 -0.103 (0.019) -5.34 2081.9 <.001 *** [-0.141, -0.065]
## ──────────────────────────────────────────────────────────
##
## Random Effects:
## ───────────────────────────────────────────
## Cluster K Parameter Variance ICC
## ───────────────────────────────────────────
## Clus 2049 (Intercept) 7.56187 0.92597
## T 0.27798
## Residual 0.60453
## ───────────────────────────────────────────4.4 Running a 1×2 model with grandmean-centered W
##
## ****************** PART 1. Regression Model Summary ******************
##
## PROCESS Model Code : 1 (Hayes, 2018; www.guilford.com/p/hayes3)
## PROCESS Model Type : Simple Moderation
## - Outcome (Y) : Y2
## - Predictor (X) : T
## - Mediators (M) : -
## - Moderators (W) : W
## - Covariates (C) : -
## - HLM Clusters : Clus
##
## Formula of Outcome:
## - Y2 ~ T*W + (T|Clus)
##
## CAUTION:
## Fixed effect (coef.) of a predictor involved in an interaction
## denotes its "simple effect/slope" at the other predictor = 0.
## Only when all predictors in an interaction are mean-centered
## can the fixed effect denote the "main effect"!
##
## Model Summary
##
## ─────────────────────────────────────────────────────
## (1) Y2 (2) Y2
## ─────────────────────────────────────────────────────
## (Intercept) 0.623 *** 1.043 ***
## (0.068) (0.131)
## T -0.054 ** -0.054
## (0.018) (0.033)
## W1 -0.568 ***
## (0.153)
## T:W1 -0.000
## (0.039)
## ─────────────────────────────────────────────────────
## Marginal R^2 0.001 0.012
## Conditional R^2 0.896 0.897
## AIC 21040.022 21022.943
## BIC 21080.027 21076.283
## Num. obs. 5811 5811
## Num. groups: Clus 2049 2049
## Var: Clus (Intercept) 7.623 7.565
## Var: Clus T 0.278 0.278
## Cov: Clus (Intercept) T -1.023 -1.024
## Var: Residual 0.605 0.605
## ─────────────────────────────────────────────────────
## Note. * p < .05, ** p < .01, *** p < .001.
##
## ************ PART 2. Mediation/Moderation Effect Estimate ************
##
## Package Use : ‘interactions’ (v1.1.5)
## Effect Type : Simple Moderation (Model 1)
## Sample Size : 5811 (223 missing observations deleted)
## Random Seed : -
## Simulations : -
##
## Interaction Effect on "Y2" (Y)
## ──────────────────────────────
## F df1 df2 p
## ──────────────────────────────
## T * W 0.00 1 1520 .990
## ──────────────────────────────
##
## Simple Slopes: "T" (X) ==> "Y2" (Y)
## ─────────────────────────────────────────────────────
## "W" Effect S.E. t p [95% CI]
## ─────────────────────────────────────────────────────
## 0 -0.054 (0.033) -1.630 .103 [-0.119, 0.011]
## 1 -0.055 (0.021) -2.650 .008 ** [-0.095, -0.014]
## ─────────────────────────────────────────────────────Interpretation of cross level results of growth model:
The intercept γ00=54.704: The predicted Y who are at the T= 0 and W = 0.
γ10 of T=-5.143: There is a significant main effect of time. Specifically, Y changes by -5.143 day for an observation that is at the W =0.
γ10 of W=-.425: There is a insignificant main effect of W, such that the expectation that observation that is higher in W are less Y at T = 0 than observations who are lower in W is not supported.
γ11 of T*W=.064: The change in the growth rate (slope of T on Y) across Clus when W increases by 1 point.
Simple slope tests (e.g., Preacher, Curran, & Bauer, 2006): This test is used to examine growth rate (i.e., relationship between T and Y) is significant at a particular value of W. T was significantly related to Y for both High-W and Low-W types. The simple slope for growth rate (slope of T on Y) is negative in Low-W group (γ = -4.061, p < .001), whereas the growth rate less negative in Low-W group (γ = −1.191, p < .05).
But since the raw value is used, it should be interpreted. The problem is that W does not have a 0 value. Therefore, it is recommended to use the value of W group centering in the analysis
4.4.1 Draw adjustment diagram
##
## Model Summary
##
## ────────────────────────────────────────────────────────────────────────────────────
## y (MLMNull) y (MLM11RR.a1) y (MLM21RR.b1) y (MLM1x2.c2)
## ────────────────────────────────────────────────────────────────────────────────────
## (Intercept) 0.53 *** 0.62 *** 1.04 *** 1.04 ***
## (0.05) (0.07) (0.10) (0.13)
## T -0.05 ** -0.05 ** -0.05
## (0.02) (0.02) (0.03)
## W1 -0.57 *** -0.57 ***
## (0.11) (0.15)
## T:W1 -0.00
## (0.04)
## ────────────────────────────────────────────────────────────────────────────────────
## Marginal R^2 0.00 0.00 0.01 0.01
## Conditional R^2 0.82 0.90 0.90 0.90
## AIC 21748.62 21040.02 21016.30 21022.94
## BIC 21768.62 21080.03 21062.97 21076.28
## Num. obs. 5811 5811 5811 5811
## Num. groups: Clus 2049 2049 2049 2049
## Var: Clus (Intercept) 4.61 7.62 7.56 7.56
## Var: Residual 1.00 0.60 0.60 0.60
## Var: Clus T 0.28 0.28 0.28
## Cov: Clus (Intercept) T -1.02 -1.02 -1.02
## ────────────────────────────────────────────────────────────────────────────────────
## Note. * p < .05, ** p < .01, *** p < .001.