Libraries
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✔ forcats 1.0.0 ✔ stringr 1.5.1
✔ ggplot2 3.4.4 ✔ tibble 3.2.1
✔ lubridate 1.9.3 ✔ tidyr 1.3.0
✔ purrr 1.0.2
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ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
Attaching package: 'magrittr'
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extract
library (lavaan) # install.packages("lavaan")
This is lavaan 0.6-17
lavaan is FREE software! Please report any bugs.
Linear model
mpg cyl disp hp drat wt qsec vs am gear carb
Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1
<- 'mpg ~ disp + hp + drat'
lm (Specification, data = mtcars) %>% summary ()
Call:
lm(formula = Specification, data = mtcars)
Residuals:
Min 1Q Median 3Q Max
-5.1225 -1.8454 -0.4456 1.1342 6.4958
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 19.344293 6.370882 3.036 0.00513 **
disp -0.019232 0.009371 -2.052 0.04960 *
hp -0.031229 0.013345 -2.340 0.02663 *
drat 2.714975 1.487366 1.825 0.07863 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 3.008 on 28 degrees of freedom
Multiple R-squared: 0.775, Adjusted R-squared: 0.7509
F-statistic: 32.15 on 3 and 28 DF, p-value: 3.28e-09
<- sem (model = Specification, data = mtcars)
summary (Model, standardized = TRUE )
lavaan 0.6.17 ended normally after 1 iteration
Estimator ML
Optimization method NLMINB
Number of model parameters 4
Number of observations 32
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
mpg ~
disp -0.019 0.009 -2.194 0.028 -0.019 -0.395
hp -0.031 0.012 -2.502 0.012 -0.031 -0.355
drat 2.715 1.391 1.951 0.051 2.715 0.241
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.mpg 7.917 1.979 4.000 0.000 7.917 0.225
Path Analysis
First example
<- ' mpg ~ disp + hp + drat hp ~ qsec + vs + am '
<- sem (model = Specification, data = mtcars)
summary (Model, standardized = TRUE , rsquare = TRUE , fit.measures = TRUE )
lavaan 0.6.17 ended normally after 1 iteration
Estimator ML
Optimization method NLMINB
Number of model parameters 8
Number of observations 32
Model Test User Model:
Test statistic 19.816
Degrees of freedom 5
P-value (Chi-square) 0.001
Model Test Baseline Model:
Test statistic 104.355
Degrees of freedom 11
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.841
Tucker-Lewis Index (TLI) 0.651
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -240.294
Loglikelihood unrestricted model (H1) -230.386
Akaike (AIC) 496.588
Bayesian (BIC) 508.314
Sample-size adjusted Bayesian (SABIC) 483.374
Root Mean Square Error of Approximation:
RMSEA 0.304
90 Percent confidence interval - lower 0.172
90 Percent confidence interval - upper 0.450
P-value H_0: RMSEA <= 0.050 0.002
P-value H_0: RMSEA >= 0.080 0.995
Standardized Root Mean Square Residual:
SRMR 0.045
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
mpg ~
disp -0.019 0.007 -2.812 0.005 -0.019 -0.407
hp -0.031 0.009 -3.295 0.001 -0.031 -0.366
drat 2.715 1.348 2.015 0.044 2.715 0.248
hp ~
qsec -26.030 6.791 -3.833 0.000 -26.030 -0.678
vs -21.111 23.771 -0.888 0.374 -21.111 -0.155
am -51.254 16.470 -3.112 0.002 -51.254 -0.373
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.mpg 7.917 1.979 4.000 0.000 7.917 0.238
.hp 1441.729 360.432 4.000 0.000 1441.729 0.317
R-Square:
Estimate
mpg 0.762
hp 0.683
= c ("srmr" , "rmsea" , "tli" , "cfi" ) fitmeasures (Model, fit.measures = GoF)
srmr rmsea tli cfi
0.045 0.304 0.651 0.841
Second example
<- ' mpg ~ disp + hp + drat hp ~ qsec + vs + am drat ~ vs + am drat ~~ disp '
<- sem (model = Specification, data = mtcars)
Warning in lav_data_full(data = data, group = group, cluster = cluster, :
lavaan WARNING: some observed variances are (at least) a factor 1000 times
larger than others; use varTable(fit) to investigate
Warning in lav_partable_vnames(FLAT, "ov.x", warn = TRUE): lavaan WARNING:
model syntax contains variance/covariance/intercept formulas
involving (an) exogenous variable(s): [disp]; These variables will
now be treated as random introducing additional free parameters.
If you wish to treat those variables as fixed, remove these
formulas from the model syntax. Otherwise, consider adding the
fixed.x = FALSE option.
summary (Model, standardized = TRUE , rsquare = TRUE , fit.measures = TRUE )
lavaan 0.6.17 ended normally after 38 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 13
Number of observations 32
Model Test User Model:
Test statistic 64.744
Degrees of freedom 9
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 182.178
Degrees of freedom 18
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.660
Tucker-Lewis Index (TLI) 0.321
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -447.841
Loglikelihood unrestricted model (H1) -415.469
Akaike (AIC) 921.682
Bayesian (BIC) 940.737
Sample-size adjusted Bayesian (SABIC) 900.210
Root Mean Square Error of Approximation:
RMSEA 0.440
90 Percent confidence interval - lower 0.343
90 Percent confidence interval - upper 0.544
P-value H_0: RMSEA <= 0.050 0.000
P-value H_0: RMSEA >= 0.080 1.000
Standardized Root Mean Square Residual:
SRMR 0.318
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
mpg ~
disp -0.019 0.004 -4.341 0.000 -0.019 -0.491
hp -0.031 0.008 -4.088 0.000 -0.031 -0.441
drat 2.715 1.223 2.220 0.026 2.715 0.259
hp ~
qsec -26.030 6.791 -3.833 0.000 -26.030 -0.678
vs -21.111 23.771 -0.888 0.374 -21.111 -0.155
am -51.254 16.470 -3.112 0.002 -51.254 -0.373
drat ~
vs 0.131 0.114 1.149 0.251 0.131 0.142
am 0.533 0.115 4.641 0.000 0.533 0.575
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.drat ~~
disp -21.079 8.593 -2.453 0.014 -21.079 -0.481
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.mpg 7.917 1.979 4.000 0.000 7.917 0.346
.hp 1441.729 360.432 4.000 0.000 1441.729 0.317
.drat 0.129 0.032 4.000 0.000 0.129 0.621
disp 14880.776 3720.194 4.000 0.000 14880.776 1.000
R-Square:
Estimate
mpg 0.654
hp 0.683
drat 0.379
SEM
PoliticalDemocracy dataset https://lavaan.ugent.be/tutorial/sem.html
y1 y2 y3 y4 y5 y6 y7 y8
1 2.50 0.000000 3.333333 0.000000 1.250000 0.000000 3.726360 3.333333
2 1.25 0.000000 3.333333 0.000000 6.250000 1.100000 6.666666 0.736999
3 7.50 8.800000 9.999998 9.199991 8.750000 8.094061 9.999998 8.211809
4 8.90 8.800000 9.999998 9.199991 8.907948 8.127979 9.999998 4.615086
5 10.00 3.333333 9.999998 6.666666 7.500000 3.333333 9.999998 6.666666
6 7.50 3.333333 6.666666 6.666666 6.250000 1.100000 6.666666 0.368500
7 7.50 3.333333 6.666666 6.666666 5.000000 2.233333 8.271257 1.485166
8 7.50 2.233333 9.999998 1.496333 6.250000 3.333333 9.999998 6.666666
9 2.50 3.333333 3.333333 3.333333 6.250000 3.333333 3.333333 3.333333
10 10.00 6.666666 9.999998 8.899991 8.750000 6.666666 9.999998 10.000000
11 7.50 3.333333 9.999998 6.666666 8.750000 3.333333 9.999998 6.666666
12 7.50 3.333333 6.666666 6.666666 8.750000 3.333333 6.666666 6.666666
13 7.50 3.333333 9.999998 6.666666 7.500000 3.333333 6.666666 10.000000
14 7.50 7.766664 9.999998 6.666666 7.500000 0.000000 9.999998 0.000000
15 7.50 9.999998 3.333333 10.000000 7.500000 6.666666 9.999998 10.000000
16 7.50 9.999998 9.999998 7.766666 7.500000 1.100000 6.666666 6.666666
17 2.50 3.333333 6.666666 6.666666 5.000000 1.100000 6.666666 0.368500
18 1.25 0.000000 3.333333 3.333333 1.250000 3.333333 3.333333 3.333333
19 10.00 9.999998 9.999998 10.000000 8.750000 9.999998 9.999998 10.000000
20 7.50 3.333299 3.333333 6.666666 7.500000 2.233299 6.666666 2.948164
21 10.00 9.999998 9.999998 10.000000 10.000000 9.999998 9.999998 10.000000
22 1.25 0.000000 0.000000 0.000000 2.500000 0.000000 0.000000 0.000000
23 2.50 0.000000 3.333333 3.333333 2.500000 0.000000 3.333333 3.333333
24 7.50 6.666666 9.999998 10.000000 7.500000 6.666666 9.999998 7.766666
25 8.50 9.999998 6.666666 6.666666 8.750000 9.999998 7.351018 6.666666
26 6.10 0.000000 5.400000 3.333333 0.000000 0.000000 4.696028 3.333333
27 3.30 0.000000 6.666666 3.333333 6.250000 0.000000 6.666666 3.333333
28 2.90 3.333333 6.666666 3.333333 2.385559 0.000000 3.177568 1.116666
29 9.20 0.000000 9.900000 3.333333 7.609660 0.000000 8.118828 3.333333
30 6.90 0.000000 6.666666 3.333333 4.226033 0.000000 0.000000 0.000000
31 2.90 0.000000 3.333333 3.333333 5.000000 0.000000 3.333333 3.333333
32 2.00 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
33 5.00 0.000000 3.333333 3.333333 5.000000 0.000000 3.333333 3.333333
34 5.00 0.000000 9.999998 3.333333 0.000000 0.000000 3.333333 0.744370
35 4.10 9.999998 4.700000 6.666666 3.750000 0.000000 7.827667 6.666666
36 6.30 9.999998 9.999998 6.666666 6.250000 2.233333 6.666666 2.955702
37 5.20 4.999998 6.600000 3.333333 3.633403 1.100000 3.314128 3.333333
38 5.00 3.333333 6.400000 6.666666 2.844997 0.000000 4.429657 1.485166
39 3.10 4.999998 4.200000 5.000000 3.750000 0.000000 6.164304 3.333333
40 4.10 9.999998 6.666666 3.333333 5.000000 0.000000 4.938089 2.233333
41 5.00 9.999998 6.666666 1.666666 5.000000 0.000000 6.666666 0.368500
42 5.00 7.700000 6.666666 8.399997 6.250000 4.358243 9.999998 4.141377
43 5.00 6.200000 9.999998 6.060997 5.000000 2.782771 6.666666 4.974739
44 5.60 4.900000 0.000000 0.000000 6.555647 4.055463 6.666666 3.821796
45 5.70 4.800000 0.000000 0.000000 6.555647 4.055463 0.000000 0.000000
46 7.50 9.999998 7.900000 6.666666 3.750000 9.999998 7.631891 6.666666
47 2.50 0.000000 6.666666 3.333333 2.500000 0.000000 0.000000 0.000000
48 8.90 9.999998 9.700000 6.666666 5.000000 9.999998 9.556024 6.666666
49 7.60 0.000000 10.000000 0.000000 5.000000 1.100000 6.666666 1.099999
50 7.80 9.999998 6.666666 6.666666 5.000000 3.333333 6.666666 6.666666
51 2.50 0.000000 6.666666 3.333333 5.000000 0.000000 6.666666 3.333333
52 3.80 0.000000 5.100000 0.000000 3.750000 0.000000 6.666666 1.485166
53 5.00 3.333333 3.333333 2.233333 5.000000 3.333333 6.666666 5.566663
54 6.25 3.333333 9.999998 2.955702 6.250000 5.566663 9.999998 6.666666
55 1.25 0.000000 3.333333 0.000000 2.500000 0.000000 0.000000 0.000000
56 1.25 0.000000 4.700000 0.736999 2.500000 0.000000 3.333333 3.333333
57 1.25 0.000000 6.666666 0.000000 2.500000 0.000000 5.228375 0.000000
58 7.50 7.766664 9.999998 6.666666 7.500000 3.333333 9.999998 6.666666
59 2.50 0.000000 6.666666 4.433333 5.000000 0.000000 6.666666 1.485166
60 7.50 9.999998 9.999998 10.000000 8.750000 9.999998 9.999998 10.000000
61 1.25 0.000000 0.000000 0.000000 1.250000 0.000000 0.000000 0.000000
62 1.25 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
63 2.50 0.000000 0.000000 0.000000 0.000000 0.000000 6.666666 2.948164
64 6.25 2.233299 6.666666 2.970332 3.750000 3.333299 6.666666 3.333333
65 7.50 9.999998 9.999998 10.000000 7.500000 9.999998 9.999998 10.000000
66 5.00 0.000000 6.100000 0.000000 5.000000 3.333333 9.999998 3.333333
67 7.50 9.999998 9.999998 10.000000 3.750000 9.999998 9.999998 10.000000
68 4.90 2.233333 9.999998 0.000000 5.000000 0.000000 3.621989 3.333333
69 5.00 0.000000 8.200000 0.000000 5.000000 0.000000 0.000000 0.000000
70 2.90 3.333333 6.666666 3.333333 2.500000 3.333333 6.666666 3.333333
71 5.40 9.999998 6.666666 3.333333 3.750000 6.666666 6.666666 1.485166
72 7.50 8.800000 9.999998 6.066666 7.500000 6.666666 9.999998 6.666666
73 7.50 7.000000 9.999998 6.852998 7.500000 6.348340 6.666666 7.508044
74 10.00 6.666666 9.999998 10.000000 10.000000 6.666666 9.999998 10.000000
75 3.75 3.333333 0.000000 0.000000 1.250000 3.333333 0.000000 0.000000
x1 x2 x3
1 4.442651 3.637586 2.557615
2 5.384495 5.062595 3.568079
3 5.961005 6.255750 5.224433
4 6.285998 7.567863 6.267495
5 5.863631 6.818924 4.573679
6 5.533389 5.135798 3.892270
7 5.308268 5.075174 3.316213
8 5.347108 4.852030 4.263183
9 5.521461 5.241747 4.115168
10 5.828946 5.370638 4.446216
11 5.916202 6.423247 3.791545
12 5.398163 6.246107 4.535708
13 6.622736 7.872074 4.906154
14 5.204007 5.225747 4.561047
15 5.509388 6.202536 4.586286
16 5.262690 5.820083 3.948911
17 4.700480 5.023881 4.394491
18 5.209486 4.465908 4.510268
19 5.916202 6.732211 5.829084
20 6.523562 6.992096 6.424591
21 6.238325 6.746412 5.741711
22 5.976351 6.712956 5.948168
23 5.631212 5.937536 5.686755
24 6.033086 6.093570 4.611429
25 6.196444 6.704414 5.475261
26 4.248495 2.708050 1.740830
27 5.141664 4.564348 2.255134
28 4.174387 3.688879 3.046927
29 4.382027 2.890372 1.711279
30 4.290459 1.609438 1.001674
31 4.934474 4.234107 1.418971
32 3.850148 1.945910 2.345229
33 5.181784 4.394449 3.167167
34 5.062595 4.595120 3.834970
35 4.691348 4.143135 2.255134
36 4.248495 3.367296 3.217506
37 5.564520 5.236442 2.677633
38 4.727388 3.610918 1.418971
39 4.143135 2.302585 1.418971
40 4.317488 4.955827 4.249888
41 5.141664 4.430817 3.046927
42 4.488636 3.465736 2.013579
43 4.615121 4.941642 2.255134
44 3.850148 2.397895 1.740830
45 3.970292 2.397895 1.050741
46 3.784190 3.091042 2.113313
47 3.806662 2.079442 2.137561
48 4.532599 3.610918 1.587802
49 5.117994 4.934474 3.834970
50 5.049856 5.111988 4.381490
51 5.393628 5.638355 4.169451
52 4.477337 3.931826 2.474671
53 5.257495 5.840642 5.001796
54 5.379897 5.505332 3.299937
55 5.298317 6.274762 4.381490
56 4.859812 5.669881 3.537416
57 4.969813 5.564520 4.510268
58 6.011267 6.253829 5.001796
59 5.075174 5.252273 5.350708
60 6.736967 7.125283 6.330518
61 5.225747 5.451038 3.167167
62 4.025352 1.791759 2.657972
63 4.234107 2.708050 2.474671
64 4.644391 5.564520 3.046927
65 4.418841 4.941642 3.380653
66 4.262680 4.219508 4.368462
67 4.875197 4.700480 3.834970
68 4.189655 1.386294 1.418971
69 4.521789 4.127134 2.113313
70 4.653960 3.555348 1.881917
71 4.477337 3.091042 1.987909
72 5.337538 5.631212 3.491004
73 6.129050 6.403574 5.001796
74 5.003946 4.962845 3.976994
75 4.488636 4.897840 2.867566
Measurement Model
<- ' ind60 =~ x1 + x2 + x3 dem60 =~ y1 + y2 + y3 + y4 dem65 =~ y5 + y6 + y7 + y8 '
<- sem (model = model, data = PoliticalDemocracy)
= c ("srmr" , "rmsea" , "tli" , "cfi" ) fitmeasures (Model, fit.measures = GoF)
srmr rmsea tli cfi
0.055 0.101 0.938 0.953
summary (Model, standardized = TRUE , rsquare = TRUE , fit.measures = TRUE )
lavaan 0.6.17 ended normally after 47 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 25
Number of observations 75
Model Test User Model:
Test statistic 72.462
Degrees of freedom 41
P-value (Chi-square) 0.002
Model Test Baseline Model:
Test statistic 730.654
Degrees of freedom 55
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.953
Tucker-Lewis Index (TLI) 0.938
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -1564.959
Loglikelihood unrestricted model (H1) -1528.728
Akaike (AIC) 3179.918
Bayesian (BIC) 3237.855
Sample-size adjusted Bayesian (SABIC) 3159.062
Root Mean Square Error of Approximation:
RMSEA 0.101
90 Percent confidence interval - lower 0.061
90 Percent confidence interval - upper 0.139
P-value H_0: RMSEA <= 0.050 0.021
P-value H_0: RMSEA >= 0.080 0.827
Standardized Root Mean Square Residual:
SRMR 0.055
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ind60 =~
x1 1.000 0.669 0.920
x2 2.182 0.139 15.714 0.000 1.461 0.973
x3 1.819 0.152 11.956 0.000 1.218 0.872
dem60 =~
y1 1.000 2.201 0.845
y2 1.354 0.175 7.755 0.000 2.980 0.760
y3 1.044 0.150 6.961 0.000 2.298 0.705
y4 1.300 0.138 9.412 0.000 2.860 0.860
dem65 =~
y5 1.000 2.084 0.803
y6 1.258 0.164 7.651 0.000 2.623 0.783
y7 1.282 0.158 8.137 0.000 2.673 0.819
y8 1.310 0.154 8.529 0.000 2.730 0.847
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ind60 ~~
dem60 0.660 0.206 3.202 0.001 0.448 0.448
dem65 0.774 0.208 3.715 0.000 0.555 0.555
dem60 ~~
dem65 4.487 0.911 4.924 0.000 0.978 0.978
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.x1 0.082 0.020 4.180 0.000 0.082 0.154
.x2 0.118 0.070 1.689 0.091 0.118 0.053
.x3 0.467 0.090 5.174 0.000 0.467 0.240
.y1 1.942 0.395 4.910 0.000 1.942 0.286
.y2 6.490 1.185 5.479 0.000 6.490 0.422
.y3 5.340 0.943 5.662 0.000 5.340 0.503
.y4 2.887 0.610 4.731 0.000 2.887 0.261
.y5 2.390 0.447 5.351 0.000 2.390 0.355
.y6 4.343 0.796 5.456 0.000 4.343 0.387
.y7 3.510 0.668 5.252 0.000 3.510 0.329
.y8 2.940 0.586 5.019 0.000 2.940 0.283
ind60 0.448 0.087 5.169 0.000 1.000 1.000
dem60 4.845 1.088 4.453 0.000 1.000 1.000
dem65 4.345 1.051 4.134 0.000 1.000 1.000
R-Square:
Estimate
x1 0.846
x2 0.947
x3 0.760
y1 0.714
y2 0.578
y3 0.497
y4 0.739
y5 0.645
y6 0.613
y7 0.671
y8 0.717
Structural Model
<- ' ind60 =~ x1 + x2 + x3 dem60 =~ y1 + y2 + y3 + y4 dem65 =~ y5 + y6 + y7 + y8 dem60 ~ ind60 dem65 ~ ind60 + dem60 '
<- sem (model = model, data = PoliticalDemocracy)
= c ("srmr" , "rmsea" , "tli" , "cfi" ) fitmeasures (Model, fit.measures = GoF)
srmr rmsea tli cfi
0.055 0.101 0.938 0.953
summary (Model, standardized = TRUE , rsquare = TRUE , fit.measures = TRUE )
lavaan 0.6.17 ended normally after 42 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 25
Number of observations 75
Model Test User Model:
Test statistic 72.462
Degrees of freedom 41
P-value (Chi-square) 0.002
Model Test Baseline Model:
Test statistic 730.654
Degrees of freedom 55
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.953
Tucker-Lewis Index (TLI) 0.938
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -1564.959
Loglikelihood unrestricted model (H1) -1528.728
Akaike (AIC) 3179.918
Bayesian (BIC) 3237.855
Sample-size adjusted Bayesian (SABIC) 3159.062
Root Mean Square Error of Approximation:
RMSEA 0.101
90 Percent confidence interval - lower 0.061
90 Percent confidence interval - upper 0.139
P-value H_0: RMSEA <= 0.050 0.021
P-value H_0: RMSEA >= 0.080 0.827
Standardized Root Mean Square Residual:
SRMR 0.055
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ind60 =~
x1 1.000 0.669 0.920
x2 2.182 0.139 15.714 0.000 1.461 0.973
x3 1.819 0.152 11.956 0.000 1.218 0.872
dem60 =~
y1 1.000 2.201 0.845
y2 1.354 0.175 7.755 0.000 2.980 0.760
y3 1.044 0.150 6.961 0.000 2.298 0.705
y4 1.300 0.138 9.412 0.000 2.860 0.860
dem65 =~
y5 1.000 2.084 0.803
y6 1.258 0.164 7.651 0.000 2.623 0.783
y7 1.282 0.158 8.137 0.000 2.673 0.819
y8 1.310 0.154 8.529 0.000 2.730 0.847
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
dem60 ~
ind60 1.474 0.392 3.763 0.000 0.448 0.448
dem65 ~
ind60 0.453 0.220 2.064 0.039 0.146 0.146
dem60 0.864 0.113 7.671 0.000 0.913 0.913
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.x1 0.082 0.020 4.180 0.000 0.082 0.154
.x2 0.118 0.070 1.689 0.091 0.118 0.053
.x3 0.467 0.090 5.174 0.000 0.467 0.240
.y1 1.942 0.395 4.910 0.000 1.942 0.286
.y2 6.490 1.185 5.479 0.000 6.490 0.422
.y3 5.340 0.943 5.662 0.000 5.340 0.503
.y4 2.887 0.610 4.731 0.000 2.887 0.261
.y5 2.390 0.447 5.351 0.000 2.390 0.355
.y6 4.343 0.796 5.456 0.000 4.343 0.387
.y7 3.510 0.668 5.252 0.000 3.510 0.329
.y8 2.940 0.586 5.019 0.000 2.940 0.283
ind60 0.448 0.087 5.169 0.000 1.000 1.000
.dem60 3.872 0.893 4.338 0.000 0.799 0.799
.dem65 0.115 0.200 0.575 0.565 0.026 0.026
R-Square:
Estimate
x1 0.846
x2 0.947
x3 0.760
y1 0.714
y2 0.578
y3 0.497
y4 0.739
y5 0.645
y6 0.613
y7 0.671
y8 0.717
dem60 0.201
dem65 0.974