Mplus model76latent 模型讲解
来自图书《MPlus中介调节模型》
Mplus潜变量调节中介模型教程结构
- 理论模型
- 数学模型
- 数学推导
- 代码解读
理论模型
数学模型
数学公式1
数学公式2
模型方程:
Y = b0 + b1M + b2MW + b3MZ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
代入和展开:
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Z + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
= b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a0b2W + a1b2XW + a2b2WW + a3b2ZW + a4b2XWW + a5b2XZW + a0b3Z + a1b3XZ + a2b3WZ + a3b3ZZ + a4b3XWZ + a5b3XZZ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ数学公式3
模型方程:
Y = b0 + b1M + b2MW + b3MZ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
代入和展开:
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Z + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
= b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a0b2W + a1b2XW + a2b2WW + a3b2ZW + a4b2XWW + a5b2XZW + a0b3Z + a1b3XZ + a2b3WZ + a3b3ZZ + a4b3XWZ + a5b3XZZ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
分组整理:
Y = (b0 + a0b1 + a2b1W + a3b1Z + a0b2W + a2b2WW + a3b2ZW + a0b3Z + a2b3WZ + a3b3ZZ + c2'W + c3'Z) + (a1b1 + a4b1W + a5b1Z + a1b2W + a4b2WW + a5b2ZW + a1b3Z + a4b3WZ + a5b3ZZ + c1' + c4'W + c5'Z)X数学公式4
模型方程:
Y = b0 + b1M + b2MW + b3MZ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
代入和展开:
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Z + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
= b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a0b2W + a1b2XW + a2b2WW + a3b2ZW + a4b2XWW + a5b2XZW + a0b3Z + a1b3XZ + a2b3WZ + a3b3ZZ + a4b3XWZ + a5b3XZZ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
分组整理:
Y = (b0 + a0b1 + a2b1W + a3b1Z + a0b2W + a2b2WW + a3b2ZW + a0b3Z + a2b3WZ + a3b3ZZ + c2'W + c3'Z) + (a1b1 + a4b1W + a5b1Z + a1b2W + a4b2WW + a5b2ZW + a1b3Z + a4b3WZ + a5b3ZZ + c1' + c4'W + c5'Z)X
间接效应:
(a1 + a4W + a5Z)(b1 + b2W + b3Z)
直接效应:
c1' + c4'W + c5'Z代码解读1
! Latent predictor variable X measured by X1-X4
! Latent mediator M measured by 4 observed variables M1-M4
! Latent moderators W and Z, each measured by sets of 4 observed variables W1-W4 and Z1-Z4 respectively
! Latent outcome variable Y measured by Y1-Y4
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;代码解读2
! Latent predictor variable X measured by X1-X4
! Latent mediator M measured by 4 observed variables M1-M4
! Latent moderators W and Z, each measured by sets of 4 observed variables W1-W4 and Z1-Z4 respectively
! Latent outcome variable Y measured by Y1-Y4
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
TYPE = GENERAL RANDOM;
ESTIMATOR = ML;
ALGORITHM = INTEGRATION;代码解读3
! Latent predictor variable X measured by X1-X4
! Latent mediator M measured by 4 observed variables M1-M4
! Latent moderators W and Z, each measured by sets of 4 observed variables W1-W4 and Z1-Z4 respectively
! Latent outcome variable Y measured by Y1-Y4
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
TYPE = GENERAL RANDOM;
ESTIMATOR = ML;
ALGORITHM = INTEGRATION;
MODEL:
! Measurement model
! Identify moderator factors by fixing variance = 1 (instead of first loading)
! This makes these factors standardised
X BY X1 X2 X3 X4;
M BY M1 M2 M3 M4;
W BY W1* W2 W3 W4;
Z BY Z1* Z2 Z3 Z4;
Y BY Y1 Y2 Y3 Y4;
W@1; Z@1;代码解读4
! Latent predictor variable X measured by X1-X4
! Latent mediator M measured by 4 observed variables M1-M4
! Latent moderators W and Z, each measured by sets of 4 observed variables W1-W4 and Z1-Z4 respectively
! Latent outcome variable Y measured by Y1-Y4
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
TYPE = GENERAL RANDOM;
ESTIMATOR = ML;
ALGORITHM = INTEGRATION;
MODEL:
! Measurement model
! Identify moderator factors by fixing variance = 1 (instead of first loading)
! This makes these factors standardised
X BY X1 X2 X3 X4;
M BY M1 M2 M3 M4;
W BY W1* W2 W3 W4;
Z BY Z1* Z2 Z3 Z4;
Y BY Y1 Y2 Y3 Y4;
W@1; Z@1;
! Create latent interactions
MW | M XWITH W;
MZ | M XWITH Z;
XW | X XWITH W;
XZ | X XWITH Z;代码解读5
! Latent predictor variable X measured by X1-X4
! Latent mediator M measured by 4 observed variables M1-M4
! Latent moderators W and Z, each measured by sets of 4 observed variables W1-W4 and Z1-Z4 respectively
! Latent outcome variable Y measured by Y1-Y4
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
TYPE = GENERAL RANDOM;
ESTIMATOR = ML;
ALGORITHM = INTEGRATION;
MODEL:
! Measurement model
! Identify moderator factors by fixing variance = 1 (instead of first loading)
! This makes these factors standardised
X BY X1 X2 X3 X4;
M BY M1 M2 M3 M4;
W BY W1* W2 W3 W4;
Z BY Z1* Z2 Z3 Z4;
Y BY Y1 Y2 Y3 Y4;
W@1; Z@1;
! Create latent interactions
MW | M XWITH W;
MZ | M XWITH Z;
XW | X XWITH W;
XZ | X XWITH Z;
! Fit structural model and name parameters
! Note that intercepts of M, Y are fixed = 0 since they are latent vars
! so no code to state and name them as parameters
Y ON M (b1);
Y ON MW (b2);
Y ON MZ (b3);
Y ON X(cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);代码解读6
! Latent predictor variable X measured by X1-X4
! Latent mediator M measured by 4 observed variables M1-M4
! Latent moderators W and Z, each measured by sets of 4 observed variables W1-W4 and Z1-Z4 respectively
! Latent outcome variable Y measured by Y1-Y4
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
TYPE = GENERAL RANDOM;
ESTIMATOR = ML;
ALGORITHM = INTEGRATION;
MODEL:
! Measurement model
! Identify moderator factors by fixing variance = 1 (instead of first loading)
! This makes these factors standardised
X BY X1 X2 X3 X4;
M BY M1 M2 M3 M4;
W BY W1* W2 W3 W4;
Z BY Z1* Z2 Z3 Z4;
Y BY Y1 Y2 Y3 Y4;
W@1; Z@1;
! Create latent interactions
MW | M XWITH W;
MZ | M XWITH Z;
XW | X XWITH W;
XZ | X XWITH Z;
! Fit structural model and name parameters
! Note that intercepts of M, Y are fixed = 0 since they are latent vars
! so no code to state and name them as parameters
Y ON M (b1);
Y ON MW (b2);
Y ON MZ (b3);
Y ON X(cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);
! Use model constraint subcommand to test conditional indirect effects
! You need to pick low, medium and high moderator values for W, Z
! for example, of 1 SD below mean, mean, 1 SD above mean
! 2 moderators, 3 values for each, gives 9 combinations
! arbitrary naming convention for conditional indirect and total effects used below:
! MEV_LOQ = medium value of V and low value of Q, etc.
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z
ILOW_LOZ IMEW_LOZ IHIW_LOZ ILOW_MEZ IMEW_MEZ IHIW_MEZ
ILOW_HIZ IMEW_HIZ IHIW_HIZ
DLOW_LOZ DMEW_LOZ DHIW_LOZ DLOW_MEZ DMEW_MEZ DHIW_MEZ
DLOW_HIZ DMEW_HIZ DHIW_HIZ
TLOW_LOZ TMEW_LOZ THIW_LOZ TLOW_MEZ TMEW_MEZ THIW_MEZ
TLOW_HIZ TMEW_HIZ THIW_HIZ);代码解读7
! Latent predictor variable X measured by X1-X4
! Latent mediator M measured by 4 observed variables M1-M4
! Latent moderators W and Z, each measured by sets of 4 observed variables W1-W4 and Z1-Z4 respectively
! Latent outcome variable Y measured by Y1-Y4
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
TYPE = GENERAL RANDOM;
ESTIMATOR = ML;
ALGORITHM = INTEGRATION;
MODEL:
! Measurement model
! Identify moderator factors by fixing variance = 1 (instead of first loading)
! This makes these factors standardised
X BY X1 X2 X3 X4;
M BY M1 M2 M3 M4;
W BY W1* W2 W3 W4;
Z BY Z1* Z2 Z3 Z4;
Y BY Y1 Y2 Y3 Y4;
W@1; Z@1;
! Create latent interactions
MW | M XWITH W;
MZ | M XWITH Z;
XW | X XWITH W;
XZ | X XWITH Z;
! Fit structural model and name parameters
! Note that intercepts of M, Y are fixed = 0 since they are latent vars
! so no code to state and name them as parameters
Y ON M (b1);
Y ON MW (b2);
Y ON MZ (b3);
Y ON X(cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);
! Use model constraint subcommand to test conditional indirect effects
! You need to pick low, medium and high moderator values for W, Z
! for example, of 1 SD below mean, mean, 1 SD above mean
! 2 moderators, 3 values for each, gives 9 combinations
! arbitrary naming convention for conditional indirect and total effects used below:
! MEV_LOQ = medium value of V and low value of Q, etc.
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z
ILOW_LOZ IMEW_LOZ IHIW_LOZ ILOW_MEZ IMEW_MEZ IHIW_MEZ
ILOW_HIZ IMEW_HIZ IHIW_HIZ
DLOW_LOZ DMEW_LOZ DHIW_LOZ DLOW_MEZ DMEW_MEZ DHIW_MEZ
DLOW_HIZ DMEW_HIZ DHIW_HIZ
TLOW_LOZ TMEW_LOZ THIW_LOZ TLOW_MEZ TMEW_MEZ THIW_MEZ
TLOW_HIZ TMEW_HIZ THIW_HIZ);
LOW_W = -1;
! -1 SD below mean value of W
MED_W = 0;
! mean value of W
HIGH_W = 1;
! +1 SD above mean value of W
LOW_Z = -1;
! -1 SD below mean value of Z
MED_Z = 0;
! mean value of Z
HIGH_Z = 1;
! +1 SD above mean value of Z代码解读8
! Latent predictor variable X measured by X1-X4
! Latent mediator M measured by 4 observed variables M1-M4
! Latent moderators W and Z, each measured by sets of 4 observed variables W1-W4 and Z1-Z4 respectively
! Latent outcome variable Y measured by Y1-Y4
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
TYPE = GENERAL RANDOM;
ESTIMATOR = ML;
ALGORITHM = INTEGRATION;
MODEL:
! Measurement model
! Identify moderator factors by fixing variance = 1 (instead of first loading)
! This makes these factors standardised
X BY X1 X2 X3 X4;
M BY M1 M2 M3 M4;
W BY W1* W2 W3 W4;
Z BY Z1* Z2 Z3 Z4;
Y BY Y1 Y2 Y3 Y4;
W@1; Z@1;
! Create latent interactions
MW | M XWITH W;
MZ | M XWITH Z;
XW | X XWITH W;
XZ | X XWITH Z;
! Fit structural model and name parameters
! Note that intercepts of M, Y are fixed = 0 since they are latent vars
! so no code to state and name them as parameters
Y ON M (b1);
Y ON MW (b2);
Y ON MZ (b3);
Y ON X(cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);
! Use model constraint subcommand to test conditional indirect effects
! You need to pick low, medium and high moderator values for W, Z
! for example, of 1 SD below mean, mean, 1 SD above mean
! 2 moderators, 3 values for each, gives 9 combinations
! arbitrary naming convention for conditional indirect and total effects used below:
! MEV_LOQ = medium value of V and low value of Q, etc.
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z
ILOW_LOZ IMEW_LOZ IHIW_LOZ ILOW_MEZ IMEW_MEZ IHIW_MEZ
ILOW_HIZ IMEW_HIZ IHIW_HIZ
DLOW_LOZ DMEW_LOZ DHIW_LOZ DLOW_MEZ DMEW_MEZ DHIW_MEZ
DLOW_HIZ DMEW_HIZ DHIW_HIZ
TLOW_LOZ TMEW_LOZ THIW_LOZ TLOW_MEZ TMEW_MEZ THIW_MEZ
TLOW_HIZ TMEW_HIZ THIW_HIZ);
LOW_W = -1;
! -1 SD below mean value of W
MED_W = 0;
! mean value of W
HIGH_W = 1;
! +1 SD above mean value of W
LOW_Z = -1;
! -1 SD below mean value of Z
MED_Z = 0;
! mean value of Z
HIGH_Z = 1;
! +1 SD above mean value of Z
! Calc conditional indirect effects for each combination of moderator values
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b2*LOW_W +
a4*b2*LOW_W*LOW_W + a5*b2*LOW_Z*LOW_W + a1*b3*LOW_Z +
a4*b3*LOW_W*LOW_Z + a5*b3*LOW_Z*LOW_Z;
IMEW_LOZ = a1*b1 + a4*b1*MED_W + a5*b1*LOW_Z + a1*b2*MED_W +
a4*b2*MED_W*MED_W + a5*b2*LOW_Z*MED_W + a1*b3*LOW_Z +
a4*b3*MED_W*LOW_Z + a5*b3*LOW_Z*LOW_Z;
IHIW_LOZ = a1*b1 + a4*b1*HIGH_W + a5*b1*LOW_Z + a1*b2*HIGH_W +
a4*b2*HIGH_W*HIGH_W + a5*b2*LOW_Z*HIGH_W + a1*b3*LOW_Z +
a4*b3*HIGH_W*LOW_Z + a5*b3*LOW_Z*LOW_Z;
... (其他条件间接效应计算)代码解读9
! Latent predictor variable X measured by X1-X4
! Latent mediator M measured by 4 observed variables M1-M4
! Latent moderators W and Z, each measured by sets of 4 observed variables W1-W4 and Z1-Z4 respectively
! Latent outcome variable Y measured by Y1-Y4
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
TYPE = GENERAL RANDOM;
ESTIMATOR = ML;
ALGORITHM = INTEGRATION;
MODEL:
! Measurement model
! Identify moderator factors by fixing variance = 1 (instead of first loading)
! This makes these factors standardised
X BY X1 X2 X3 X4;
M BY M1 M2 M3 M4;
W BY W1* W2 W3 W4;
Z BY Z1* Z2 Z3 Z4;
Y BY Y1 Y2 Y3 Y4;
W@1; Z@1;
! Create latent interactions
MW | M XWITH W;
MZ | M XWITH Z;
XW | X XWITH W;
XZ | X XWITH Z;
! Fit structural model and name parameters
! Note that intercepts of M, Y are fixed = 0 since they are latent vars
! so no code to state and name them as parameters
Y ON M (b1);
Y ON MW (b2);
Y ON MZ (b3);
Y ON X(cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);
! Use model constraint subcommand to test conditional indirect effects
! You need to pick low, medium and high moderator values for W, Z
! for example, of 1 SD below mean, mean, 1 SD above mean
! 2 moderators, 3 values for each, gives 9 combinations
! arbitrary naming convention for conditional indirect and total effects used below:
! MEV_LOQ = medium value of V and low value of Q, etc.
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z
ILOW_LOZ IMEW_LOZ IHIW_LOZ ILOW_MEZ IMEW_MEZ IHIW_MEZ
ILOW_HIZ IMEW_HIZ IHIW_HIZ
DLOW_LOZ DMEW_LOZ DHIW_LOZ DLOW_MEZ DMEW_MEZ DHIW_MEZ
DLOW_HIZ DMEW_HIZ DHIW_HIZ
TLOW_LOZ TMEW_LOZ THIW_LOZ TLOW_MEZ TMEW_MEZ THIW_MEZ
TLOW_HIZ TMEW_HIZ THIW_HIZ);
LOW_W = -1;
! -1 SD below mean value of W
MED_W = 0;
! mean value of W
HIGH_W = 1;
! +1 SD above mean value of W
LOW_Z = -1;
! -1 SD below mean value of Z
MED_Z = 0;
! mean value of Z
HIGH_Z = 1;
! +1 SD above mean value of Z
! Calc conditional indirect effects for each combination of moderator values
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b2*LOW_W +
a4*b2*LOW_W*LOW_W + a5*b2*LOW_Z*LOW_W + a1*b3*LOW_Z +
a4*b3*LOW_W*LOW_Z + a5*b3*LOW_Z*LOW_Z;
IMEW_LOZ = a1*b1 + a4*b1*MED_W + a5*b1*LOW_Z + a1*b2*MED_W +
a4*b2*MED_W*MED_W + a5*b2*LOW_Z*MED_W + a1*b3*LOW_Z +
a4*b3*MED_W*LOW_Z + a5*b3*LOW_Z*LOW_Z;
IHIW_LOZ = a1*b1 + a4*b1*HIGH_W + a5*b1*LOW_Z + a1*b2*HIGH_W +
a4*b2*HIGH_W*HIGH_W + a5*b2*LOW_Z*HIGH_W + a1*b3*LOW_Z +
a4*b3*HIGH_W*LOW_Z + a5*b3*LOW_Z*LOW_Z;
... (其他条件间接效应计算)
! Calc conditional direct effects for each combination of moderator values
DLOW_LOZ = cdash1 + cdash4*LOW_W + cdash5*LOW_Z;
DMEW_LOZ = cdash1 + cdash4*MED_W + cdash5*LOW_Z;
DHIW_LOZ = cdash1 + cdash4*HIGH_W + cdash5*LOW_Z;
... (其他条件直接效应计算)代码解读10
! Latent predictor variable X measured by X1-X4
! Latent mediator M measured by 4 observed variables M1-M4
! Latent moderators W and Z, each measured by sets of 4 observed variables W1-W4 and Z1-Z4 respectively
! Latent outcome variable Y measured by Y1-Y4
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
TYPE = GENERAL RANDOM;
ESTIMATOR = ML;
ALGORITHM = INTEGRATION;
MODEL:
! Measurement model
! Identify moderator factors by fixing variance = 1 (instead of first loading)
! This makes these factors standardised
X BY X1 X2 X3 X4;
M BY M1 M2 M3 M4;
W BY W1* W2 W3 W4;
Z BY Z1* Z2 Z3 Z4;
Y BY Y1 Y2 Y3 Y4;
W@1; Z@1;
! Create latent interactions
MW | M XWITH W;
MZ | M XWITH Z;
XW | X XWITH W;
XZ | X XWITH Z;
! Fit structural model and name parameters
! Note that intercepts of M, Y are fixed = 0 since they are latent vars
! so no code to state and name them as parameters
Y ON M (b1);
Y ON MW (b2);
Y ON MZ (b3);
Y ON X(cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);
! Use model constraint subcommand to test conditional indirect effects
! You need to pick low, medium and high moderator values for W, Z
! for example, of 1 SD below mean, mean, 1 SD above mean
! 2 moderators, 3 values for each, gives 9 combinations
! arbitrary naming convention for conditional indirect and total effects used below:
! MEV_LOQ = medium value of V and low value of Q, etc.
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z
ILOW_LOZ IMEW_LOZ IHIW_LOZ ILOW_MEZ IMEW_MEZ IHIW_MEZ
ILOW_HIZ IMEW_HIZ IHIW_HIZ
DLOW_LOZ DMEW_LOZ DHIW_LOZ DLOW_MEZ DMEW_MEZ DHIW_MEZ
DLOW_HIZ DMEW_HIZ DHIW_HIZ
TLOW_LOZ TMEW_LOZ THIW_LOZ TLOW_MEZ TMEW_MEZ THIW_MEZ
TLOW_HIZ TMEW_HIZ THIW_HIZ);
LOW_W = -1;
! -1 SD below mean value of W
MED_W = 0;
! mean value of W
HIGH_W = 1;
! +1 SD above mean value of W
LOW_Z = -1;
! -1 SD below mean value of Z
MED_Z = 0;
! mean value of Z
HIGH_Z = 1;
! +1 SD above mean value of Z
! Calc conditional indirect effects for each combination of moderator values
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b2*LOW_W +
a4*b2*LOW_W*LOW_W + a5*b2*LOW_Z*LOW_W + a1*b3*LOW_Z +
a4*b3*LOW_W*LOW_Z + a5*b3*LOW_Z*LOW_Z;
IMEW_LOZ = a1*b1 + a4*b1*MED_W + a5*b1*LOW_Z + a1*b2*MED_W +
a4*b2*MED_W*MED_W + a5*b2*LOW_Z*MED_W + a1*b3*LOW_Z +
a4*b3*MED_W*LOW_Z + a5*b3*LOW_Z*LOW_Z;
IHIW_LOZ = a1*b1 + a4*b1*HIGH_W + a5*b1*LOW_Z + a1*b2*HIGH_W +
a4*b2*HIGH_W*HIGH_W + a5*b2*LOW_Z*HIGH_W + a1*b3*LOW_Z +
a4*b3*HIGH_W*LOW_Z + a5*b3*LOW_Z*LOW_Z;
... (其他条件间接效应计算)
! Calc conditional direct effects for each combination of moderator values
DLOW_LOZ = cdash1 + cdash4*LOW_W + cdash5*LOW_Z;
DMEW_LOZ = cdash1 + cdash4*MED_W + cdash5*LOW_Z;
DHIW_LOZ = cdash1 + cdash4*HIGH_W + cdash5*LOW_Z;
... (其他条件直接效应计算)
! Calc conditional total effects for each combination of moderator values
TLOW_LOZ = ILOW_LOZ + DLOW_LOZ;
TMEW_LOZ = IMEW_LOZ + DMEW_LOZ;
THIW_LOZ = IHIW_LOZ + DHIW_LOZ;
... (其他条件总效应计算)代码解读11
! Latent predictor variable X measured by X1-X4
! Latent mediator M measured by 4 observed variables M1-M4
! Latent moderators W and Z, each measured by sets of 4 observed variables W1-W4 and Z1-Z4 respectively
! Latent outcome variable Y measured by Y1-Y4
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
TYPE = GENERAL RANDOM;
ESTIMATOR = ML;
ALGORITHM = INTEGRATION;
MODEL:
! Measurement model
! Identify moderator factors by fixing variance = 1 (instead of first loading)
! This makes these factors standardised
X BY X1 X2 X3 X4;
M BY M1 M2 M3 M4;
W BY W1* W2 W3 W4;
Z BY Z1* Z2 Z3 Z4;
Y BY Y1 Y2 Y3 Y4;
W@1; Z@1;
! Create latent interactions
MW | M XWITH W;
MZ | M XWITH Z;
XW | X XWITH W;
XZ | X XWITH Z;
! Fit structural model and name parameters
! Note that intercepts of M, Y are fixed = 0 since they are latent vars
! so no code to state and name them as parameters
Y ON M (b1);
Y ON MW (b2);
Y ON MZ (b3);
Y ON X(cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);
! Use model constraint subcommand to test conditional indirect effects
! You need to pick low, medium and high moderator values for W, Z
! for example, of 1 SD below mean, mean, 1 SD above mean
! 2 moderators, 3 values for each, gives 9 combinations
! arbitrary naming convention for conditional indirect and total effects used below:
! MEV_LOQ = medium value of V and low value of Q, etc.
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z
ILOW_LOZ IMEW_LOZ IHIW_LOZ ILOW_MEZ IMEW_MEZ IHIW_MEZ
ILOW_HIZ IMEW_HIZ IHIW_HIZ
DLOW_LOZ DMEW_LOZ DHIW_LOZ DLOW_MEZ DMEW_MEZ DHIW_MEZ
DLOW_HIZ DMEW_HIZ DHIW_HIZ
TLOW_LOZ TMEW_LOZ THIW_LOZ TLOW_MEZ TMEW_MEZ THIW_MEZ
TLOW_HIZ TMEW_HIZ THIW_HIZ);
LOW_W = -1;
! -1 SD below mean value of W
MED_W = 0;
! mean value of W
HIGH_W = 1;
! +1 SD above mean value of W
LOW_Z = -1;
! -1 SD below mean value of Z
MED_Z = 0;
! mean value of Z
HIGH_Z = 1;
! +1 SD above mean value of Z
! Calc conditional indirect effects for each combination of moderator values
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b2*LOW_W +
a4*b2*LOW_W*LOW_W + a5*b2*LOW_Z*LOW_W + a1*b3*LOW_Z +
a4*b3*LOW_W*LOW_Z + a5*b3*LOW_Z*LOW_Z;
IMEW_LOZ = a1*b1 + a4*b1*MED_W + a5*b1*LOW_Z + a1*b2*MED_W +
a4*b2*MED_W*MED_W + a5*b2*LOW_Z*MED_W + a1*b3*LOW_Z +
a4*b3*MED_W*LOW_Z + a5*b3*LOW_Z*LOW_Z;
IHIW_LOZ = a1*b1 + a4*b1*HIGH_W + a5*b1*LOW_Z + a1*b2*HIGH_W +
a4*b2*HIGH_W*HIGH_W + a5*b2*LOW_Z*HIGH_W + a1*b3*LOW_Z +
a4*b3*HIGH_W*LOW_Z + a5*b3*LOW_Z*LOW_Z;
... (其他条件间接效应计算)
! Calc conditional direct effects for each combination of moderator values
DLOW_LOZ = cdash1 + cdash4*LOW_W + cdash5*LOW_Z;
DMEW_LOZ = cdash1 + cdash4*MED_W + cdash5*LOW_Z;
DHIW_LOZ = cdash1 + cdash4*HIGH_W + cdash5*LOW_Z;
... (其他条件直接效应计算)
! Calc conditional total effects for each combination of moderator values
TLOW_LOZ = ILOW_LOZ + DLOW_LOZ;
TMEW_LOZ = IMEW_LOZ + DMEW_LOZ;
THIW_LOZ = IHIW_LOZ + DHIW_LOZ;
... (其他条件总效应计算)
! Use loop plot to plot conditional indirect effect of X on Y for each combination of low, med, high moderator values
! Could be edited to show conditional direct or conditional total effects instead
! NOTE - values from -3 to 3 in LOOP() statement since
! X is factor with mean set at default of 0
PLOT(PLOW_LOZ PMEW_LOZ PHIW_LOZ PLOW_MEZ PMEW_MEZ PHIW_MEZ
PLOW_HIZ PMEW_HIZ PHIW_HIZ);
LOOP(XVAL,-3,3,0.1);
PLOW_LOZ = ILOW_LOZ*XVAL;
PMEW_LOZ = IMEW_LOZ*XVAL;
PHIW_LOZ = IHIW_LOZ*XVAL;
...(其他条件间接效应绘图)代码解读12
! Latent predictor variable X measured by X1-X4
! Latent mediator M measured by 4 observed variables M1-M4
! Latent moderators W and Z, each measured by sets of 4 observed variables W1-W4 and Z1-Z4 respectively
! Latent outcome variable Y measured by Y1-Y4
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
TYPE = GENERAL RANDOM;
ESTIMATOR = ML;
ALGORITHM = INTEGRATION;
MODEL:
! Measurement model
! Identify moderator factors by fixing variance = 1 (instead of first loading)
! This makes these factors standardised
X BY X1 X2 X3 X4;
M BY M1 M2 M3 M4;
W BY W1* W2 W3 W4;
Z BY Z1* Z2 Z3 Z4;
Y BY Y1 Y2 Y3 Y4;
W@1; Z@1;
! Create latent interactions
MW | M XWITH W;
MZ | M XWITH Z;
XW | X XWITH W;
XZ | X XWITH Z;
! Fit structural model and name parameters
! Note that intercepts of M, Y are fixed = 0 since they are latent vars
! so no code to state and name them as parameters
Y ON M (b1);
Y ON MW (b2);
Y ON MZ (b3);
Y ON X(cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);
! Use model constraint subcommand to test conditional indirect effects
! You need to pick low, medium and high moderator values for W, Z
! for example, of 1 SD below mean, mean, 1 SD above mean
! 2 moderators, 3 values for each, gives 9 combinations
! arbitrary naming convention for conditional indirect and total effects used below:
! MEV_LOQ = medium value of V and low value of Q, etc.
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z
ILOW_LOZ IMEW_LOZ IHIW_LOZ ILOW_MEZ IMEW_MEZ IHIW_MEZ
ILOW_HIZ IMEW_HIZ IHIW_HIZ
DLOW_LOZ DMEW_LOZ DHIW_LOZ DLOW_MEZ DMEW_MEZ DHIW_MEZ
DLOW_HIZ DMEW_HIZ DHIW_HIZ
TLOW_LOZ TMEW_LOZ THIW_LOZ TLOW_MEZ TMEW_MEZ THIW_MEZ
TLOW_HIZ TMEW_HIZ THIW_HIZ);
LOW_W = -1;
! -1 SD below mean value of W
MED_W = 0;
! mean value of W
HIGH_W = 1;
! +1 SD above mean value of W
LOW_Z = -1;
! -1 SD below mean value of Z
MED_Z = 0;
! mean value of Z
HIGH_Z = 1;
! +1 SD above mean value of Z
! Calc conditional indirect effects for each combination of moderator values
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b2*LOW_W +
a4*b2*LOW_W*LOW_W + a5*b2*LOW_Z*LOW_W + a1*b3*LOW_Z +
a4*b3*LOW_W*LOW_Z + a5*b3*LOW_Z*LOW_Z;
IMEW_LOZ = a1*b1 + a4*b1*MED_W + a5*b1*LOW_Z + a1*b2*MED_W +
a4*b2*MED_W*MED_W + a5*b2*LOW_Z*MED_W + a1*b3*LOW_Z +
a4*b3*MED_W*LOW_Z + a5*b3*LOW_Z*LOW_Z;
IHIW_LOZ = a1*b1 + a4*b1*HIGH_W + a5*b1*LOW_Z + a1*b2*HIGH_W +
a4*b2*HIGH_W*HIGH_W + a5*b2*LOW_Z*HIGH_W + a1*b3*LOW_Z +
a4*b3*HIGH_W*LOW_Z + a5*b3*LOW_Z*LOW_Z;
... (其他条件间接效应计算)
! Calc conditional direct effects for each combination of moderator values
DLOW_LOZ = cdash1 + cdash4*LOW_W + cdash5*LOW_Z;
DMEW_LOZ = cdash1 + cdash4*MED_W + cdash5*LOW_Z;
DHIW_LOZ = cdash1 + cdash4*HIGH_W + cdash5*LOW_Z;
... (其他条件直接效应计算)
! Calc conditional total effects for each combination of moderator values
TLOW_LOZ = ILOW_LOZ + DLOW_LOZ;
TMEW_LOZ = IMEW_LOZ + DMEW_LOZ;
THIW_LOZ = IHIW_LOZ + DHIW_LOZ;
... (其他条件总效应计算)
! Use loop plot to plot conditional indirect effect of X on Y for each combination of low, med, high moderator values
! Could be edited to show conditional direct or conditional total effects instead
! NOTE - values from -3 to 3 in LOOP() statement since
! X is factor with mean set at default of 0
PLOT(PLOW_LOZ PMEW_LOZ PHIW_LOZ PLOW_MEZ PMEW_MEZ PHIW_MEZ
PLOW_HIZ PMEW_HIZ PHIW_HIZ);
LOOP(XVAL,-3,3,0.1);
PLOW_LOZ = ILOW_LOZ*XVAL;
PMEW_LOZ = IMEW_LOZ*XVAL;
PHIW_LOZ = IHIW_LOZ*XVAL;
...(其他条件间接效应绘图)
PLOT:
TYPE = plot2;
OUTPUT:
CINT;