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. 2019 Nov 21;19:858. doi: 10.1186/s12913-019-4609-9

Table 5.

Results of all models

Level Parameters and Variables Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7
Fixed Effect
Level 1 Initial efficiency (π0ij)
Intercept (γ000)

0.829***

(0.017)

0.798***

(0.021)

0.792***

(0.022)

0.798***

(0.019)

0.843***

(0.068)

0.695***

(0.092)

0.823***

(0.061)
Linear growth rate (T, π1ij)
Intercept (β100)

0.016**

(0.005)

0.028*

(0.011)
Nonlinear growth rate (T2, π2ij)

−0.003

(0.003)
Intercept (β200)
FP (π2ij)

0.337**

(0.103)

0.324**

(0.099)
A2 (π3ij)

0.000***

(0.000)

0.000

(0.000)
A3 (π4ij)

0.000

(0.001)

0.000

(0.001)
A6 (π5ij)

−0.001

(0.003)

−0.006*

(0.002)
A11 (π6ij)

0.000

(0.000)

0.000

(0.000)
V1 (π7ij)

0.119**

(0.044)

0.114**

(0.042)
V7 (π8ij)

−12.491**

(4.575)

−10.366*

(4.555)
V8 (π9ij)

0.038**

(0.014)

0.041**

(0.013)
V9 (π10ij)

−0.001

(0.001)

−0.001

(0.001)
V10 (π11ij)

0.000

(0.001)

0.000

(0.001)
T × A2 (π12ij)

0.000

(0.000)
T × A3 (π13ij)

0.000

(0.001)
T × A6 (π14ij)

0.003**

(0.001)
T × A11 (π15ij)

0.000

(0.000)
Level 2 GHP (β01j)

−0.025

(0.024)

0.027

(0.025)

−0.042

(0.024)
IHP (β02j)

0.019

(0.049)

0.037

(0.048)

0.043

(0.046)
ZY (β03j)

−0.079*

(0.038)

− 0.078*

(0.037)

− 0.063

(0.035)
FY (β04j)

0.073

(0.056)

0.097

(0.055)

0.117*

(0.052)
Level 3 GDP (γ001)

0.000

(0.000)

0.000

(0.000)

0.003

(0.003)

0.003

(0.003)
D1 (γ002)

0.003

(0.021)

0.006

(0.024)

0.001

(0.025)

0.002

(0.026)
DP (γ003)

1.105

(0.699)

0.753

(0.842)

1.216

(0.782)

1.224

(0.779)
HP (γ004)

−0.103

(0.141)

−0.050

(0.149)

−0.092

(0.129)

− 0.105

(0.133)
CZ (γ005)

−0.005

(0.003)

−0.004

(0.003)

− 0.005

(0.003)

−0.005

(0.003)

Growth rate

(T, π0ij)
Intercept (γ100)

0.016**

(0.005)

0.028*

(0.011)

0.016**

(0.005)

0.020

(0.190)

0.023

(0.026)

0.025*

(0.013)
Level 2 GHP (β11j)

−0.001

(0.005)

0.001

(0.004)

0.004

(0.004)
IHP (β11j)

0.003

(0.014)

−0.006

(0.013)

−0.009

(0.013)
ZY (β11j)

0.013

(0.011)

0.011

(0.011)

0.008

(0.008)
FY (β11j)

−0.019

(0.015)

−0.032

(0.018)

− 0.036**

(0.014)
Level 3 GDP (γ101)

0.000

(0.000)

0.000

(0.000)

−0.001

(0.001)

−0.001

(0.001)
D1 (γ102)

0.007*

(0.003)

0.007*

(0.003)

0.009*

(0.004)

0.009*

(0.004)
DP (γ103)

−0.075

(0.157)

− 0.095

(0.187)

−0.332*

(0.169)

− 0.310

(0.175)
HP (γ104)

−0.016

(0.031)

−0.013

(0.034)

0.009

(0.029)

0.007

(0.029)
CZ (γ105)

0.000

(0.001)

0.000

(0.001)

0.001

(0.001)

0.001

(0.001)
Variance Components
σ2 Initial efficiency

0.011***

(0.001)

0.008***

(0.001)

0.007***

(0.000)

0.008***

(0.001)

0.008***

(0.001)

0.007***

(0.001)

0.006***

(0.001)
σ2r0 Initial efficiency

0.012***

(0.002)

0.021***

(0.004)

0.020***

(0.000)

0.021***

(0.004)

0.014***

(0.003)

0.013***

(0.003)

0.012***

(0.003)
Growth rate

0.001**

(0.000)

0.004

(0.000)

0.001**

(0.000)

0.001

(0.000)

0.001*

(0.000)

0.000*

(0.000)
σ2u0 Initial efficiency

0.002

(0.002)

0.002

(0.003)

0.003

(0.003)

0.001

(0.004)

0.002

(0.003)

0.002

(0.002)

0.003

(0.003)
Growth rate

0.000**

(0.000)

0.000

(0.000)

0.000

(0.000)

0.000

(0.000)

0.000

(0.000)

0.000

(0.000)
Covariance
Level 2 Initial efficiency and growth rate

−0.003**

(0.001)

−0.002

(0.002)

−0.003**

(0.001)

−0.002

(0.001)

−0.001

(0.001)

−0.001

(0.001)
Level 3

0.000

(0.000)

−0.001

(0.001)

0.000

(0.001)

0.000

(0.001)

0.000

(0.000)

0.000

(0.001)
Model fit Np 4 9 16 19 27 37 41
LL 228.239 247.529 250.324 251.646 260.718 292.292 302.857
AIC − 448.490 − 477.059 − 468.649 −465.291 −467.436 − 510.584 −523.713
BIC − 432.946 − 442.084 − 406.471 − 392.455 − 362.511 −366.798 − 364.383
ICC Level 2 0.482
Level 3 0.081

Note: * p < 0.05, ** p < 0.01, and *** p < 0.001. Np the model estimation parameter, LL logarithmic likelihood ratio, AIC Akaike information criterion, BIC Bayesian information criterion, ICC intraclass correlation coefficient