For the first part, the documentation provides an example

```
library(lavaan)
#> This is lavaan 0.6-5
#> lavaan is BETA software! Please report any bugs.
example(cfa)
#>
#> cfa> ## The famous Holzinger and Swineford (1939) example
#> cfa> HS.model <- ' visual =~ x1 + x2 + x3
#> cfa+ textual =~ x4 + x5 + x6
#> cfa+ speed =~ x7 + x8 + x9 '
#>
#> cfa> fit <- cfa(HS.model, data = HolzingerSwineford1939)
#>
#> cfa> summary(fit, fit.measures = TRUE)
#> lavaan 0.6-5 ended normally after 35 iterations
#>
#> Estimator ML
#> Optimization method NLMINB
#> Number of free parameters 21
#>
#> Number of observations 301
#>
#> Model Test User Model:
#>
#> Test statistic 85.306
#> Degrees of freedom 24
#> P-value (Chi-square) 0.000
#>
#> Model Test Baseline Model:
#>
#> Test statistic 918.852
#> Degrees of freedom 36
#> P-value 0.000
#>
#> User Model versus Baseline Model:
#>
#> Comparative Fit Index (CFI) 0.931
#> Tucker-Lewis Index (TLI) 0.896
#>
#> Loglikelihood and Information Criteria:
#>
#> Loglikelihood user model (H0) -3737.745
#> Loglikelihood unrestricted model (H1) -3695.092
#>
#> Akaike (AIC) 7517.490
#> Bayesian (BIC) 7595.339
#> Sample-size adjusted Bayesian (BIC) 7528.739
#>
#> Root Mean Square Error of Approximation:
#>
#> RMSEA 0.092
#> 90 Percent confidence interval - lower 0.071
#> 90 Percent confidence interval - upper 0.114
#> P-value RMSEA <= 0.05 0.001
#>
#> Standardized Root Mean Square Residual:
#>
#> SRMR 0.065
#>
#> Parameter Estimates:
#>
#> Information Expected
#> Information saturated (h1) model Structured
#> Standard errors Standard
#>
#> Latent Variables:
#> Estimate Std.Err z-value P(>|z|)
#> visual =~
#> x1 1.000
#> x2 0.554 0.100 5.554 0.000
#> x3 0.729 0.109 6.685 0.000
#> textual =~
#> x4 1.000
#> x5 1.113 0.065 17.014 0.000
#> x6 0.926 0.055 16.703 0.000
#> speed =~
#> x7 1.000
#> x8 1.180 0.165 7.152 0.000
#> x9 1.082 0.151 7.155 0.000
#>
#> Covariances:
#> Estimate Std.Err z-value P(>|z|)
#> visual ~~
#> textual 0.408 0.074 5.552 0.000
#> speed 0.262 0.056 4.660 0.000
#> textual ~~
#> speed 0.173 0.049 3.518 0.000
#>
#> Variances:
#> Estimate Std.Err z-value P(>|z|)
#> .x1 0.549 0.114 4.833 0.000
#> .x2 1.134 0.102 11.146 0.000
#> .x3 0.844 0.091 9.317 0.000
#> .x4 0.371 0.048 7.779 0.000
#> .x5 0.446 0.058 7.642 0.000
#> .x6 0.356 0.043 8.277 0.000
#> .x7 0.799 0.081 9.823 0.000
#> .x8 0.488 0.074 6.573 0.000
#> .x9 0.566 0.071 8.003 0.000
#> visual 0.809 0.145 5.564 0.000
#> textual 0.979 0.112 8.737 0.000
#> speed 0.384 0.086 4.451 0.000
```

^{Created on 2020-01-14 by the reprex package (v0.3.0)}

*And* there is a `tutorial`

that came out yesterday! But that is many a `how to operate`

, than `how to intepret`

. For that we need to go to the paper

The second part of your question, using the same data, is represented by this `reprex`

```
library(lavaan)
#> This is lavaan 0.6-5
#> lavaan is BETA software! Please report any bugs.
HS.model <- '
visual =~ x1 + b1*x2 + x3
textual =~ x4 + b2*x5 + x6
speed =~ x7 + b3*x8 + x9
b1 == b2
b2 == b3 '
fit <- cfa(HS.model, data=HolzingerSwineford1939)
lavTestScore(fit, cumulative = TRUE)
#> $test
#>
#> total score test:
#>
#> test X2 df p.value
#> 1 score 12.306 2 0.002
#>
#> $uni
#>
#> univariate score tests:
#>
#> lhs op rhs X2 df p.value
#> 1 b1 == b2 12.060 1 0.001
#> 2 b2 == b3 0.947 1 0.330
#>
#> $cumulative
#>
#> cumulative score tests:
#>
#> lhs op rhs X2 df p.value
#> 1 b1 == b2 12.060 1 0.001
#> 2 b2 == b3 12.306 2 0.002
```

^{Created on 2020-01-14 by the reprex package (v0.3.0)}

There's a lot to unpack here about the interpretation of the output. I'm still studying it. Some are fairly standard (lower `AIC`

better than higher, *ceteris paribus*), but I'll need some more time to answer your specific questions.

In the meantime, I hope others can weigh in on the interpretation using these `reprex`

s