LEADER DAILY DELEGATION AND PERFORMANCE
Prof. Yucheng Zhang
2024-12-05
2 DATA PREPARATION
2.1 Load all sheets of an Excel
X: Leader delegation=LDLV Level-1 Moderator [Mo1]: Leader emotional exhaustion =LEDV Level-2 Moderator [Mo2]: LMX=LMX
Mediator [M]: Follower work engagement =MWEV Y: Follower task performance(t+1)=LPERFV2
Controls: [C1] Interaction Freuencey=MIFV, [C2] Follower work engagement (t-1)=MWEV0, [C4] Leader delegation(t-1)=LDLV0, [C5] Leader emotional exhaustion (t-1)=LEDV0, [C3] Follower task performance(t-1)=LPERFV0
2.2 Same day: All group mean centered
## Error: 在 'old' 中未找到如下列名：[LPERF.GroC]。请考虑设置 skip_absent=TRUE。2.3 Reproduce HRs (f - mod lmx.out): All group mean centered
X=LDLV0; !leader delegation
C0=MIFV0;
C1=MIFV;
C2=MWEV0;
C3=LPERFV0;
C4=LDLV;
C5=LEDV;
!C6=LPERFV;
!Mo1=LEEHV0; !leader emotionale exhaustion
Mo2=MLMXP; !LSABP;
Me=MWEV;
Y=LPERFV2;
CENTER X(GROUPMEAN);
!CENTER X Mo1(GROUPMEAN);
!Inter1 = X*Mo1;
CENTER Mo2 (GRANDMEAN);2.4 Same day: All group mean centered
## Error: 在 'old' 中未找到如下列名：[LDLV.GroC, LEDV.GroC, MWEV.GroC]。请考虑设置 skip_absent=TRUE。IV: LDLV Level-1 Moderator: LEDV Level-2 Moderator: LMX Mediator: MWEV DV: LPERFV2 Controls: MIFV, MWEV0, LDLV0, LEDV0, LPERFV0
##
## ------ Sample Size Information ------
##
## Level 1: N = 1071 observations ("X")
## Level 2: K = 106 groups ("MNum")
##
## n (group sizes)
## Min. 6.0
## Median 10.0
## Mean 10.1
## Max. 16.0
##
## ------ ICC(1), ICC(2), and rWG ------
##
## ICC variable: "X"
##
## ICC(1) = 0.000 (non-independence of data)
## ICC(2) = 0.000 (reliability of group means)
##
## rWG variable: "X"
##
## rWG (within-group agreement for single-item measures)
## ─────────────────────────────────────────────
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## ─────────────────────────────────────────────
## rWG 0.103 0.782 0.866 0.833 0.920 1.000
## ─────────────────────────────────────────────
##
##
## ------ Sample Size Information ------
##
## Level 1: N = 1071 observations ("Mo1")
## Level 2: K = 106 groups ("MNum")
##
## n (group sizes)
## Min. 6.0
## Median 10.0
## Mean 10.1
## Max. 16.0
##
## ------ ICC(1), ICC(2), and rWG ------
##
## ICC variable: "Mo1"
##
## ICC(1) = 0.000 (non-independence of data)
## ICC(2) = 0.000 (reliability of group means)
##
## rWG variable: "Mo1"
##
## rWG (within-group agreement for single-item measures)
## ─────────────────────────────────────────────
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## ─────────────────────────────────────────────
## rWG 0.000 0.760 0.914 0.845 0.979 1.000
## ─────────────────────────────────────────────## Error in eval_f(x, ...): Downdated VtV is not positive definite3 PATH A
##
## Hierarchical Linear Model (HLM)
## (also known as) Linear Mixed Model (LMM)
## (also known as) Multilevel Linear Model (MLM)
##
## Model Information:
## Formula: M ~ X * Mo1 + X * Mo2 + C1 + (X | MNum)
## Level-1 Observations: N = 1008
## Level-2 Groups/Clusters: MNum, 104
##
## Model Fit:
## AIC = 2928.464
## BIC = 2982.537
## R_(m)² = 0.03661 (Marginal R²: fixed effects)
## R_(c)² = 0.64390 (Conditional R²: fixed + random effects)
## Omega² = 0.68315 (= 1 - proportion of unexplained variance)
##
## ANOVA Table:
## ──────────────────────────────────────────────────
## Sum Sq Mean Sq NumDF DenDF F p
## ──────────────────────────────────────────────────
## X 0.89 0.89 1.00 53.92 1.14 .290
## Mo1 0.43 0.43 1.00 908.11 0.56 .455
## Mo2 0.62 0.62 1.00 104.74 0.80 .373
## C1 58.09 58.09 1.00 826.63 74.62 <.001 ***
## X:Mo1 3.10 3.10 1.00 716.52 3.98 .046 *
## X:Mo2 3.74 3.74 1.00 45.83 4.80 .033 *
## ──────────────────────────────────────────────────
##
## Fixed Effects:
## Unstandardized Coefficients (b or γ):
## Outcome Variable: M
## ─────────────────────────────────────────────────────────────────
## b/γ S.E. t df p [95% CI of b/γ]
## ─────────────────────────────────────────────────────────────────
## (Intercept) 5.199 (0.116) 44.72 104.4 <.001 *** [ 4.968, 5.429]
## X 0.041 (0.038) 1.07 53.9 .290 [-0.036, 0.117]
## Mo1 -0.029 (0.039) -0.75 908.1 .455 [-0.104, 0.047]
## Mo2 0.091 (0.102) 0.89 104.7 .373 [-0.111, 0.293]
## C1 0.206 (0.024) 8.64 826.6 <.001 *** [ 0.159, 0.253]
## X:Mo1 0.125 (0.063) 1.99 716.5 .046 * [ 0.002, 0.247]
## X:Mo2 0.075 (0.034) 2.19 45.8 .033 * [ 0.006, 0.143]
## ─────────────────────────────────────────────────────────────────
## 'df' is estimated by Satterthwaite approximation.
##
## Standardized Coefficients (β):
## Outcome Variable: M
## ───────────────────────────────────────────────────────────
## β S.E. t df p [95% CI of β]
## ───────────────────────────────────────────────────────────
## X 0.021 (0.020) 1.07 53.9 .290 [-0.019, 0.061]
## Mo1 -0.014 (0.019) -0.75 908.1 .455 [-0.052, 0.023]
## Mo2 0.069 (0.078) 0.89 104.7 .373 [-0.085, 0.224]
## C1 0.163 (0.019) 8.64 826.6 <.001 *** [ 0.126, 0.200]
## X:Mo1 0.041 (0.020) 1.99 716.5 .046 * [ 0.001, 0.081]
## X:Mo2 0.043 (0.020) 2.19 45.8 .033 * [ 0.004, 0.083]
## ───────────────────────────────────────────────────────────
##
## Random Effects:
## ──────────────────────────────────────────
## Cluster K Parameter Variance ICC
## ──────────────────────────────────────────
## MNum 104 (Intercept) 1.32196 0.62939
## X 0.00991
## Residual 0.77844
## ──────────────────────────────────────────
4 PATH B
##
## Hierarchical Linear Model (HLM)
## (also known as) Linear Mixed Model (LMM)
## (also known as) Multilevel Linear Model (MLM)
##
## Model Information:
## Formula: Y ~ M + X + C1 + (X | MNum)
## Level-1 Observations: N = 907
## Level-2 Groups/Clusters: MNum, 104
##
## Model Fit:
## AIC = 2507.561
## BIC = 2546.043
## R_(m)² = 0.00549 (Marginal R²: fixed effects)
## R_(c)² = 0.72476 (Conditional R²: fixed + random effects)
## Omega² = NA (= 1 - proportion of unexplained variance)
##
## ANOVA Table:
## ──────────────────────────────────────────────
## Sum Sq Mean Sq NumDF DenDF F p
## ──────────────────────────────────────────────
## M 2.80 2.80 1.00 893.62 4.53 .033 *
## X 1.61 1.61 1.00 123.27 2.62 .108
## C1 1.15 1.15 1.00 810.83 1.86 .173
## ──────────────────────────────────────────────
##
## Fixed Effects:
## Unstandardized Coefficients (b or γ):
## Outcome Variable: Y
## ─────────────────────────────────────────────────────────────────
## b/γ S.E. t df p [95% CI of b/γ]
## ─────────────────────────────────────────────────────────────────
## (Intercept) 4.758 (0.205) 23.27 449.5 <.001 *** [ 4.356, 5.160]
## M 0.066 (0.031) 2.13 893.6 .033 * [ 0.005, 0.127]
## X 0.069 (0.042) 1.62 123.3 .108 [-0.015, 0.153]
## C1 -0.033 (0.024) -1.36 810.8 .173 [-0.080, 0.014]
## ─────────────────────────────────────────────────────────────────
## 'df' is estimated by Satterthwaite approximation.
##
## Standardized Coefficients (β):
## Outcome Variable: Y
## ────────────────────────────────────────────────────────
## β S.E. t df p [95% CI of β]
## ────────────────────────────────────────────────────────
## M 0.062 (0.029) 2.13 893.6 .033 * [ 0.005, 0.120]
## X 0.034 (0.021) 1.62 123.3 .108 [-0.008, 0.076]
## C1 -0.025 (0.018) -1.36 810.8 .173 [-0.060, 0.011]
## ────────────────────────────────────────────────────────
##
## Random Effects:
## ──────────────────────────────────────────
## Cluster K Parameter Variance ICC
## ──────────────────────────────────────────
## MNum 104 (Intercept) 1.58739 0.72002
## X 0.04272
## Residual 0.61725
## ──────────────────────────────────────────##
## Model Summary
##
## ───────────────────────────────────────────────────
## (1) M (2) Y
## ───────────────────────────────────────────────────
## (Intercept) 5.199 *** 4.758 ***
## (0.116) (0.205)
## X 0.041 0.069
## (0.038) (0.042)
## Mo1 -0.029
## (0.039)
## Mo2 0.091
## (0.102)
## C1 0.206 *** -0.033
## (0.024) (0.024)
## X:Mo1 0.125 *
## (0.063)
## X:Mo2 0.075 *
## (0.034)
## M 0.066 *
## (0.031)
## ───────────────────────────────────────────────────
## Marginal R^2 0.037 0.005
## Conditional R^2 0.644 0.725
## AIC 2928.464 2507.561
## BIC 2982.537 2546.043
## Num. obs. 1008 907
## Num. groups: MNum 104 104
## Var: MNum (Intercept) 1.322 1.587
## Var: MNum X 0.010 0.043
## Cov: MNum (Intercept) X -0.096 0.005
## Var: Residual 0.778 0.617
## ───────────────────────────────────────────────────
## Note. * p < .05, ** p < .01, *** p < .001.
##
## Effects of Mediation (rep=5000, seed=1223 if not preset):
## ────────────────────────────────────────────────────────────────────────────────────
## Effects ab SEab a SEa b SEb abLLCI abULCI sig
## ────────────────────────────────────────────────────────────────────────────────────
## 1 Monte Carlo based Mediation 0.008 0.006 0.125 0.063 0.066 0.031 -0.001 0.022 no
## 2 Monte Carlo based Mediation 0.005 0.003 0.075 0.034 0.066 0.031 -0.000 0.013 no
## ────────────────────────────────────────────────────────────────────────────────────