Can anyone help with the interpretation of lisreal outputs shown in the image below.
What does it all mean really? What do all the different numbers in the diagram represent in simple terms?
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TI
Covariance Matrix
SELECT3A SELECT3B SELECT3C SELECT2A SELECT2C SELECT2B
-------- -------- -------- -------- -------- --------
SELECT3A 1.06
SELECT3B 0.89 1.29
SELECT3C 0.86 0.92 1.58
SELECT2A 0.11 0.15 0.44 1.31
SELECT2C 0.16 0.16 0.47 0.95 1.22
SELECT2B 0.17 0.22 0.45 0.90 0.79 1.16
SELECT4A 0.40 0.38 0.58 0.33 0.39 0.28
SELECT4D 0.40 0.38 0.50 0.31 0.32 0.18
SELECT4C 0.46 0.36 0.53 0.26 0.24 0.20
SELECT4B 0.52 0.48 0.62 0.38 0.40 0.30
SELECT1D 0.27 0.34 0.35 0.33 0.24 0.29
SELECT1C 0.38 0.41 0.50 0.44 0.36 0.37
SELECT1B 0.21 0.22 0.35 0.39 0.19 0.28
SELECT1A 0.21 0.15 0.38 0.25 0.15 0.22
Covariance Matrix
SELECT4A SELECT4D SELECT4C SELECT4B SELECT1D SELECT1C
-------- -------- -------- -------- -------- --------
SELECT4A 1.38
SELECT4D 0.95 1.44
SELECT4C 0.79 1.06 1.47
SELECT4B 0.97 1.08 1.08 1.52
SELECT1D 0.28 0.35 0.25 0.55 1.41
SELECT1C 0.40 0.40 0.17 0.40 0.93 1.48
SELECT1B 0.18 0.21 0.05 0.30 0.79 1.08
SELECT1A 0.28 0.35 0.12 0.33 0.79 1.11
Covariance Matrix
SELECT1B SELECT1A
-------- --------
SELECT1B 1.21
SELECT1A 1.10 1.41
TI
Parameter Specifications
LAMBDA-X
Strat fl Prototyp Differ R Foster R
-------- -------- -------- --------
SELECT3A 1 0 0 0
SELECT3B 2 0 0 0
SELECT3C 3 0 0 0
SELECT2A 0 4 0 0
SELECT2C 0 5 0 0
SELECT2B 0 6 0 0
SELECT4A 0 0 7 0
SELECT4D 0 0 8 0
SELECT4C 0 0 9 0
SELECT4B 0 0 10 0
SELECT1D 0 0 0 11
SELECT1C 0 0 0 12
SELECT1B 0 0 0 13
SELECT1A 0 0 0 14
PHI
Strat fl Prototyp Differ R Foster R
-------- -------- -------- --------
Strat fl 0
Prototyp 15 0
Differ R 16 17 0
Foster R 18 19 20 0
THETA-DELTA
SELECT3A SELECT3B SELECT3C SELECT2A SELECT2C SELECT2B
-------- -------- -------- -------- -------- --------
21 22 23 24 25 26
THETA-DELTA
SELECT4A SELECT4D SELECT4C SELECT4B SELECT1D SELECT1C
-------- -------- -------- -------- -------- --------
27 28 29 30 31 32
THETA-DELTA
SELECT1B SELECT1A
-------- --------
33 34
TI
Number of Iterations = 10
LISREL Estimates (Maximum Likelihood)
LAMBDA-X
Strat fl Prototyp Differ R Foster R
-------- -------- -------- --------
SELECT3A 0.92 - - - - - -
(0.09)
9.98
SELECT3B 0.97 - - - - - -
(0.10)
9.35
SELECT3C 0.96 - - - - - -
(0.12)
8.06
SELECT2A - - 1.05 - - - -
(0.10)
10.51
SELECT2C - - 0.91 - - - -
(0.10)
8.96
SELECT2B - - 0.86 - - - -
(0.10)
8.73
SELECT4A - - - - 0.89 - -
(0.11)
8.07
SELECT4D - - - - 1.03 - -
(0.11)
9.79
SELECT4C - - - - 0.99 - -
(0.11)
9.00
SELECT4B - - - - 1.08 - -
(0.11)
10.02
SELECT1D - - - - - - 0.79
(0.11)
6.92
SELECT1C - - - - - - 1.07
(0.10)
10.23
SELECT1B - - - - - - 1.02
(0.09)
11.31
SELECT1A - - - - - - 1.05
(0.10)
10.45
PHI
Strat fl Prototyp Differ R Foster R
-------- -------- -------- --------
Strat fl 1.00
Prototyp 0.22 1.00
(0.11)
1.92
Differ R 0.48 0.32 1.00
(0.10) (0.11)
5.03 2.93
Foster R 0.29 0.31 0.26 1.00
(0.11) (0.11) (0.11)
2.67 2.95 2.36
THETA-DELTA
SELECT3A SELECT3B SELECT3C SELECT2A SELECT2C SELECT2B
-------- -------- -------- -------- -------- --------
0.22 0.36 0.66 0.21 0.40 0.41
(0.07) (0.09) (0.12) (0.08) (0.08) (0.08)
3.17 4.09 5.40 2.57 4.81 5.04
THETA-DELTA
SELECT4A SELECT4D SELECT4C SELECT4B SELECT1D SELECT1C
-------- -------- -------- -------- -------- --------
0.59 0.37 0.49 0.36 0.78 0.35
(0.10) (0.08) (0.09) (0.08) (0.13) (0.07)
5.70 4.56 5.23 4.30 6.25 4.97
THETA-DELTA
SELECT1B SELECT1A
-------- --------
0.16 0.30
(0.05) (0.06)
3.42 4.73
Squared Multiple Correlations for X - Variables
SELECT3A SELECT3B SELECT3C SELECT2A SELECT2C SELECT2B
-------- -------- -------- -------- -------- --------
0.79 0.72 0.58 0.84 0.67 0.65
Squared Multiple Correlations for X - Variables
SELECT4A SELECT4D SELECT4C SELECT4B SELECT1D SELECT1C
-------- -------- -------- -------- -------- --------
0.57 0.74 0.66 0.76 0.45 0.77
Squared Multiple Correlations for X - Variables
SELECT1B SELECT1A
-------- --------
0.87 0.79
Goodness of Fit Statistics
Degrees of Freedom = 71
Minimum Fit Function Chi-Square = 84.04 (P = 0.14)
Normal Theory Weighted Least Squares Chi-Square = 78.62 (P = 0.25)
Estimated Non-centrality Parameter (NCP) = 7.62
90 Percent Confidence Interval for NCP = (0.0 ; 33.46)
Minimum Fit Function Value = 0.95
Population Discrepancy Function Value (F0) = 0.087
90 Percent Confidence Interval for F0 = (0.0 ; 0.38)
Root Mean Square Error of Approximation (RMSEA) = 0.035
90 Percent Confidence Interval for RMSEA = (0.0 ; 0.073)
P-Value for Test of Close Fit (RMSEA < 0.05) = 0.70
Chi-Square for Independence Model with 91 Degrees of Freedom = 1177.44
Normed Fit Index (NFI) = 0.93
Non-Normed Fit Index (NNFI) = 0.98
Comparative Fit Index (CFI) = 0.99
Incremental Fit Index (IFI) = 0.99
Relative Fit Index (RFI) = 0.91
What does it all mean really? What do all the different numbers in the diagram represent in simple terms?
TI
Covariance Matrix
SELECT3A SELECT3B SELECT3C SELECT2A SELECT2C SELECT2B
-------- -------- -------- -------- -------- --------
SELECT3A 1.06
SELECT3B 0.89 1.29
SELECT3C 0.86 0.92 1.58
SELECT2A 0.11 0.15 0.44 1.31
SELECT2C 0.16 0.16 0.47 0.95 1.22
SELECT2B 0.17 0.22 0.45 0.90 0.79 1.16
SELECT4A 0.40 0.38 0.58 0.33 0.39 0.28
SELECT4D 0.40 0.38 0.50 0.31 0.32 0.18
SELECT4C 0.46 0.36 0.53 0.26 0.24 0.20
SELECT4B 0.52 0.48 0.62 0.38 0.40 0.30
SELECT1D 0.27 0.34 0.35 0.33 0.24 0.29
SELECT1C 0.38 0.41 0.50 0.44 0.36 0.37
SELECT1B 0.21 0.22 0.35 0.39 0.19 0.28
SELECT1A 0.21 0.15 0.38 0.25 0.15 0.22
Covariance Matrix
SELECT4A SELECT4D SELECT4C SELECT4B SELECT1D SELECT1C
-------- -------- -------- -------- -------- --------
SELECT4A 1.38
SELECT4D 0.95 1.44
SELECT4C 0.79 1.06 1.47
SELECT4B 0.97 1.08 1.08 1.52
SELECT1D 0.28 0.35 0.25 0.55 1.41
SELECT1C 0.40 0.40 0.17 0.40 0.93 1.48
SELECT1B 0.18 0.21 0.05 0.30 0.79 1.08
SELECT1A 0.28 0.35 0.12 0.33 0.79 1.11
Covariance Matrix
SELECT1B SELECT1A
-------- --------
SELECT1B 1.21
SELECT1A 1.10 1.41
TI
Parameter Specifications
LAMBDA-X
Strat fl Prototyp Differ R Foster R
-------- -------- -------- --------
SELECT3A 1 0 0 0
SELECT3B 2 0 0 0
SELECT3C 3 0 0 0
SELECT2A 0 4 0 0
SELECT2C 0 5 0 0
SELECT2B 0 6 0 0
SELECT4A 0 0 7 0
SELECT4D 0 0 8 0
SELECT4C 0 0 9 0
SELECT4B 0 0 10 0
SELECT1D 0 0 0 11
SELECT1C 0 0 0 12
SELECT1B 0 0 0 13
SELECT1A 0 0 0 14
PHI
Strat fl Prototyp Differ R Foster R
-------- -------- -------- --------
Strat fl 0
Prototyp 15 0
Differ R 16 17 0
Foster R 18 19 20 0
THETA-DELTA
SELECT3A SELECT3B SELECT3C SELECT2A SELECT2C SELECT2B
-------- -------- -------- -------- -------- --------
21 22 23 24 25 26
THETA-DELTA
SELECT4A SELECT4D SELECT4C SELECT4B SELECT1D SELECT1C
-------- -------- -------- -------- -------- --------
27 28 29 30 31 32
THETA-DELTA
SELECT1B SELECT1A
-------- --------
33 34
TI
Number of Iterations = 10
LISREL Estimates (Maximum Likelihood)
LAMBDA-X
Strat fl Prototyp Differ R Foster R
-------- -------- -------- --------
SELECT3A 0.92 - - - - - -
(0.09)
9.98
SELECT3B 0.97 - - - - - -
(0.10)
9.35
SELECT3C 0.96 - - - - - -
(0.12)
8.06
SELECT2A - - 1.05 - - - -
(0.10)
10.51
SELECT2C - - 0.91 - - - -
(0.10)
8.96
SELECT2B - - 0.86 - - - -
(0.10)
8.73
SELECT4A - - - - 0.89 - -
(0.11)
8.07
SELECT4D - - - - 1.03 - -
(0.11)
9.79
SELECT4C - - - - 0.99 - -
(0.11)
9.00
SELECT4B - - - - 1.08 - -
(0.11)
10.02
SELECT1D - - - - - - 0.79
(0.11)
6.92
SELECT1C - - - - - - 1.07
(0.10)
10.23
SELECT1B - - - - - - 1.02
(0.09)
11.31
SELECT1A - - - - - - 1.05
(0.10)
10.45
PHI
Strat fl Prototyp Differ R Foster R
-------- -------- -------- --------
Strat fl 1.00
Prototyp 0.22 1.00
(0.11)
1.92
Differ R 0.48 0.32 1.00
(0.10) (0.11)
5.03 2.93
Foster R 0.29 0.31 0.26 1.00
(0.11) (0.11) (0.11)
2.67 2.95 2.36
THETA-DELTA
SELECT3A SELECT3B SELECT3C SELECT2A SELECT2C SELECT2B
-------- -------- -------- -------- -------- --------
0.22 0.36 0.66 0.21 0.40 0.41
(0.07) (0.09) (0.12) (0.08) (0.08) (0.08)
3.17 4.09 5.40 2.57 4.81 5.04
THETA-DELTA
SELECT4A SELECT4D SELECT4C SELECT4B SELECT1D SELECT1C
-------- -------- -------- -------- -------- --------
0.59 0.37 0.49 0.36 0.78 0.35
(0.10) (0.08) (0.09) (0.08) (0.13) (0.07)
5.70 4.56 5.23 4.30 6.25 4.97
THETA-DELTA
SELECT1B SELECT1A
-------- --------
0.16 0.30
(0.05) (0.06)
3.42 4.73
Squared Multiple Correlations for X - Variables
SELECT3A SELECT3B SELECT3C SELECT2A SELECT2C SELECT2B
-------- -------- -------- -------- -------- --------
0.79 0.72 0.58 0.84 0.67 0.65
Squared Multiple Correlations for X - Variables
SELECT4A SELECT4D SELECT4C SELECT4B SELECT1D SELECT1C
-------- -------- -------- -------- -------- --------
0.57 0.74 0.66 0.76 0.45 0.77
Squared Multiple Correlations for X - Variables
SELECT1B SELECT1A
-------- --------
0.87 0.79
Goodness of Fit Statistics
Degrees of Freedom = 71
Minimum Fit Function Chi-Square = 84.04 (P = 0.14)
Normal Theory Weighted Least Squares Chi-Square = 78.62 (P = 0.25)
Estimated Non-centrality Parameter (NCP) = 7.62
90 Percent Confidence Interval for NCP = (0.0 ; 33.46)
Minimum Fit Function Value = 0.95
Population Discrepancy Function Value (F0) = 0.087
90 Percent Confidence Interval for F0 = (0.0 ; 0.38)
Root Mean Square Error of Approximation (RMSEA) = 0.035
90 Percent Confidence Interval for RMSEA = (0.0 ; 0.073)
P-Value for Test of Close Fit (RMSEA < 0.05) = 0.70
Chi-Square for Independence Model with 91 Degrees of Freedom = 1177.44
Normed Fit Index (NFI) = 0.93
Non-Normed Fit Index (NNFI) = 0.98
Comparative Fit Index (CFI) = 0.99
Incremental Fit Index (IFI) = 0.99
Relative Fit Index (RFI) = 0.91