Use a better baseline model by default

[yrosseel]

By default, lavaan uses the independence model as the baseline model, in order to compute fit indices like TLI and CFI. A custom baseline model can be passed on, but perhaps there is a better/universal way to build a baseline model that is always nested within the user model.

An initial attempt is made in the function lav_object_baseline() (in lav_object_generate.R). But it still needs work.

[vsavalei]

Adding stuff from your email (March 10 2026) here:

library(lavaan)
HS.model <- ' visual  =~ x1 + x2 + x3
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9 '

fit <- cfa(HS.model, data = HolzingerSwineford1939, baseline.type = "nested")

You can check the parameter table for the baseline model as follows:

as.data.frame(fit@baseline$partable)

and the resulting test statistics as

fit@baseline$test[[1]]

Or, to see more details, you can explicitly fit and inspect the baseline model as follows:

fit0 <- lavaan:::lav_object_baseline(fit)
summary(fit0)

Instead of generating the baseline/independence model from scratch (which is still the default), the "nested" approach takes the user h0 model, and imposes some restrictions (by altering the parameter table). In particular:

• all directed effects (factor loadings and regressions) are fixed to zero
• all covariances are fixed to zero
• the latent variances are set to zero (so they have no effect)

But everything else (including equality constraints) is kept. So by design, the resulting baseline model should always be nested (in the parameter sense) within the original h0 model.

[vsavalei]

My comments from March on the above setup. It's great but for models with mean structures, customization would still be required.

To yield the recommended baseline model with multiple groups, we would want to force factor means to zero as well. Under the change above, they continue to be estimated (and depending on H1, can result in a non-nested baseline model).

The hardest case is the growth curve model. Under the change above, the slope factor still has a non-zero mean, so it forces a trend through the observed means. This is considered to be too relaxed for a baseline model, and might result in artificially poor fit. However, if you force the factor means to zero, it will force observed means to all be zero. This may overshoot the other way and be too restrictive (but at least it remains nested). The most recommended baseline model in the literature is equal observed means. This would mean setting the Random Slope factor mean to 0 but keeping the mean of the Random Intercept free (or freeing observed variable's intercepts while constraining them to equal).

This is all I have in old notes.