The summary() function gives a nice overview of a fitted model, but is for
display only. If you need the actual numbers for further processing, you may
prefer to use one of several ‘extractor’ functions. We have already seen the
coef() function which extracts the estimated parameters of a fitted model.
Other extractor functions are discussed below.
The parameterEstimates() function returns a data.frame containing
all the model parameters in the rows:
fit <- cfa(HS.model, data=HolzingerSwineford1939)
parameterEstimates(fit)
lhs op rhs est se z pvalue ci.lower ci.upper
1 visual =~ x1 1.000 0.000 NA NA 1.000 1.000
2 visual =~ x2 0.554 0.100 5.554 0 0.358 0.749
3 visual =~ x3 0.729 0.109 6.685 0 0.516 0.943
4 textual =~ x4 1.000 0.000 NA NA 1.000 1.000
5 textual =~ x5 1.113 0.065 17.014 0 0.985 1.241
6 textual =~ x6 0.926 0.055 16.703 0 0.817 1.035
7 speed =~ x7 1.000 0.000 NA NA 1.000 1.000
8 speed =~ x8 1.180 0.165 7.152 0 0.857 1.503
9 speed =~ x9 1.082 0.151 7.155 0 0.785 1.378
10 x1 ~~ x1 0.549 0.114 4.833 0 0.326 0.772
11 x2 ~~ x2 1.134 0.102 11.146 0 0.934 1.333
12 x3 ~~ x3 0.844 0.091 9.317 0 0.667 1.022
13 x4 ~~ x4 0.371 0.048 7.779 0 0.278 0.465
14 x5 ~~ x5 0.446 0.058 7.642 0 0.332 0.561
15 x6 ~~ x6 0.356 0.043 8.277 0 0.272 0.441
16 x7 ~~ x7 0.799 0.081 9.823 0 0.640 0.959
17 x8 ~~ x8 0.488 0.074 6.573 0 0.342 0.633
18 x9 ~~ x9 0.566 0.071 8.003 0 0.427 0.705
19 visual ~~ visual 0.809 0.145 5.564 0 0.524 1.094
20 textual ~~ textual 0.979 0.112 8.737 0 0.760 1.199
21 speed ~~ speed 0.384 0.086 4.451 0 0.215 0.553
22 visual ~~ textual 0.408 0.074 5.552 0 0.264 0.552
23 visual ~~ speed 0.262 0.056 4.660 0 0.152 0.373
24 textual ~~ speed 0.173 0.049 3.518 0 0.077 0.270
The lhs (left-hand side), op (operator) and rhs (right-hand side) columns
define the parameter. The est, se, z and pvalue columns provide the
point estimate, the standard error, the z-value and the p-value for this
parameter. The last two columns are the lower and upper bounds of a 95%
confidence interval around the point estimate.
The standardizedSolution() function is similar to the parameterEstimates()
function, but only shows the standardized parameter estimates and corresponding
standard errors, z-values, p-values and confidence intervals.
The fitted() and fitted.values() functions return the
model-implied (fitted) covariance matrix (and mean vector) of a fitted model:
fit <- cfa(HS.model, data = HolzingerSwineford1939)
fitted(fit)
$cov
x1 x2 x3 x4 x5 x6 x7 x8 x9
x1 1.358
x2 0.448 1.382
x3 0.590 0.327 1.275
x4 0.408 0.226 0.298 1.351
x5 0.454 0.252 0.331 1.090 1.660
x6 0.378 0.209 0.276 0.907 1.010 1.196
x7 0.262 0.145 0.191 0.173 0.193 0.161 1.183
x8 0.309 0.171 0.226 0.205 0.228 0.190 0.453 1.022
x9 0.284 0.157 0.207 0.188 0.209 0.174 0.415 0.490 1.015
The resid() or residuals() functions return (unstandardized) residuals of a
fitted model. This is simply the difference between the observed and implied
covariance matrix and mean vector.
fit <- cfa(HS.model, data = HolzingerSwineford1939)
resid(fit)
$type
[1] "raw"
$cov
x1 x2 x3 x4 x5 x6 x7 x8 x9
x1 0.000
x2 -0.041 0.000
x3 -0.010 0.124 0.000
x4 0.097 -0.017 -0.090 0.000
x5 -0.014 -0.040 -0.219 0.008 0.000
x6 0.077 0.038 -0.032 -0.012 0.005 0.000
x7 -0.177 -0.242 -0.103 0.046 -0.050 -0.017 0.000
x8 -0.046 -0.062 -0.013 -0.079 -0.047 -0.024 0.082 0.000
x9 0.175 0.087 0.167 0.056 0.086 0.062 -0.042 -0.032 0.000
The lavResiduals() gives more extensive information about the residuals.
Per default, it will print both raw and standardized residuals, as well
as several summary statistics (including the SRMR and the unbiased SRMR).
The function vcov() returns the estimated covariance matrix of the parameter
estimates.
The AIC() and BIC() functions return the AIC and BIC values of a fitted
model.
The fitMeasures() function returns all the fit measures computed by lavaan as
a named numeric vector.
fit <- cfa(HS.model, data=HolzingerSwineford1939)
fitMeasures(fit)
npar fmin chisq df
21.000 0.142 85.306 24.000
pvalue baseline.chisq baseline.df baseline.pvalue
0.000 918.852 36.000 0.000
cfi tli nnfi rfi
0.931 0.896 0.896 0.861
nfi pnfi ifi rni
0.907 0.605 0.931 0.931
logl unrestricted.logl aic bic
-3737.745 -3695.092 7517.490 7595.339
ntotal bic2 rmsea rmsea.ci.lower
301.000 7528.739 0.092 0.071
rmsea.ci.upper rmsea.pvalue rmr rmr_nomean
0.114 0.001 0.082 0.082
srmr srmr_bentler srmr_bentler_nomean crmr
0.065 0.065 0.065 0.073
crmr_nomean srmr_mplus srmr_mplus_nomean cn_05
0.073 0.065 0.065 129.490
cn_01 gfi agfi pgfi
152.654 0.943 0.894 0.503
mfi ecvi
0.903 0.423
If you only want the value of a single fit measure, say, the CFI, you give the name (in lower case) as the second argument:
fit <- cfa(HS.model, data=HolzingerSwineford1939)
fitMeasures(fit, "cfi")
cfi
0.931
Or you can provide a vector of fit measures, as in
fitMeasures(fit, c("cfi","rmsea","srmr"))
cfi rmsea srmr
0.931 0.092 0.065
If you want to peek inside a fitted lavaan object (the object that is returned
by a call to cfa(), sem()or growth()), you can use the lavInspect()
function, with a variety of options. By default, calling lavInspect() on a
fitted lavaan object returns a list of the model matrices that are used
internally to represent the model. The free parameters are nonzero integers.
fit <- cfa(HS.model, data=HolzingerSwineford1939)
lavInspect(fit)
$lambda
visual textul speed
x1 0 0 0
x2 1 0 0
x3 2 0 0
x4 0 0 0
x5 0 3 0
x6 0 4 0
x7 0 0 0
x8 0 0 5
x9 0 0 6
$theta
x1 x2 x3 x4 x5 x6 x7 x8 x9
x1 7
x2 0 8
x3 0 0 9
x4 0 0 0 10
x5 0 0 0 0 11
x6 0 0 0 0 0 12
x7 0 0 0 0 0 0 13
x8 0 0 0 0 0 0 0 14
x9 0 0 0 0 0 0 0 0 15
$psi
visual textul speed
visual 16
textual 19 17
speed 20 21 18
To see the starting values of parameters in each model matrix, type
lavInspect(fit, what = "start")
$lambda
visual textul speed
x1 1.000 0.000 0.000
x2 0.778 0.000 0.000
x3 1.107 0.000 0.000
x4 0.000 1.000 0.000
x5 0.000 1.133 0.000
x6 0.000 0.924 0.000
x7 0.000 0.000 1.000
x8 0.000 0.000 1.225
x9 0.000 0.000 0.854
$theta
x1 x2 x3 x4 x5 x6 x7 x8 x9
x1 0.679
x2 0.000 0.691
x3 0.000 0.000 0.637
x4 0.000 0.000 0.000 0.675
x5 0.000 0.000 0.000 0.000 0.830
x6 0.000 0.000 0.000 0.000 0.000 0.598
x7 0.000 0.000 0.000 0.000 0.000 0.000 0.592
x8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.511
x9 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.508
$psi
visual textul speed
visual 0.05
textual 0.00 0.05
speed 0.00 0.00 0.05
To see how lavaan internally represents a model, you can type
lavInspect(fit, what = "list")
id lhs op rhs user block group free ustart exo label plabel start
1 1 visual =~ x1 1 1 1 0 1 0 .p1. 1.000
2 2 visual =~ x2 1 1 1 1 NA 0 .p2. 0.778
3 3 visual =~ x3 1 1 1 2 NA 0 .p3. 1.107
4 4 textual =~ x4 1 1 1 0 1 0 .p4. 1.000
5 5 textual =~ x5 1 1 1 3 NA 0 .p5. 1.133
6 6 textual =~ x6 1 1 1 4 NA 0 .p6. 0.924
7 7 speed =~ x7 1 1 1 0 1 0 .p7. 1.000
8 8 speed =~ x8 1 1 1 5 NA 0 .p8. 1.225
9 9 speed =~ x9 1 1 1 6 NA 0 .p9. 0.854
10 10 x1 ~~ x1 0 1 1 7 NA 0 .p10. 0.679
11 11 x2 ~~ x2 0 1 1 8 NA 0 .p11. 0.691
12 12 x3 ~~ x3 0 1 1 9 NA 0 .p12. 0.637
13 13 x4 ~~ x4 0 1 1 10 NA 0 .p13. 0.675
14 14 x5 ~~ x5 0 1 1 11 NA 0 .p14. 0.830
15 15 x6 ~~ x6 0 1 1 12 NA 0 .p15. 0.598
16 16 x7 ~~ x7 0 1 1 13 NA 0 .p16. 0.592
17 17 x8 ~~ x8 0 1 1 14 NA 0 .p17. 0.511
18 18 x9 ~~ x9 0 1 1 15 NA 0 .p18. 0.508
19 19 visual ~~ visual 0 1 1 16 NA 0 .p19. 0.050
20 20 textual ~~ textual 0 1 1 17 NA 0 .p20. 0.050
21 21 speed ~~ speed 0 1 1 18 NA 0 .p21. 0.050
22 22 visual ~~ textual 0 1 1 19 NA 0 .p22. 0.000
23 23 visual ~~ speed 0 1 1 20 NA 0 .p23. 0.000
24 24 textual ~~ speed 0 1 1 21 NA 0 .p24. 0.000
est se
1 1.000 0.000
2 0.554 0.100
3 0.729 0.109
4 1.000 0.000
5 1.113 0.065
6 0.926 0.055
7 1.000 0.000
8 1.180 0.165
9 1.082 0.151
10 0.549 0.114
11 1.134 0.102
12 0.844 0.091
13 0.371 0.048
14 0.446 0.058
15 0.356 0.043
16 0.799 0.081
17 0.488 0.074
18 0.566 0.071
19 0.809 0.145
20 0.979 0.112
21 0.384 0.086
22 0.408 0.074
23 0.262 0.056
24 0.173 0.049
This is equivalent to the parTable(fit) function. The table that
is returned here is called the ‘parameter table’.
For more lavInspect options, see the help page:
?lavInspect