LLChisq in GAMs differ from example

[dumaskvn]

Hi !
First many thanks for maintaining this amazing package.

I recently got interested in using gam models within SEMs built with piecewise (althought this is not going well due to #293 ).

While going through your excellent book (https://jslefche.github.io/sem_book/local-estimation.html#extensions-to-non-linear-models), I noticed that log-likelihood Chi2 values differ between the book and the actual results.

set.seed(100)
n <- 100
x1 <- rchisq(n, 7)
mu2 <- 10*x1/(5 + x1)
x2 <- rnorm(n, mu2, 1)
x2[x2 <= 0] <- 0.1
x3 <- rpois(n, lambda = (0.5*x2))
x4 <- rpois(n, lambda = (0.5*x2))
p.x5 <- exp(-0.5*x3 + 0.5*x4)/(1 + exp(-0.5*x3 + 0.5*x4))
x5 <- rbinom(n, size = 1, prob = p.x5)
dat2 <- data.frame(x1 = x1, x2 = x2, x3 = x3, x4 = x4, x5 = x5)

library(mgcv)
#> Loading required package: nlme
#> This is mgcv 1.9-1. For overview type 'help("mgcv-package")'.
library(piecewiseSEM)
#> 
#>   This is piecewiseSEM version 2.3.0.
#> 
#> 
#>   Questions or bugs can be addressed to <[email protected]>.

shipley_psem2 <- psem(
  lm(x2 ~ x1, data = dat2),
  lm(x3 ~ x2, data = dat2),
  lm(x4 ~ x2, data = dat2),
  lm(x5 ~ x3 + x4, data = dat2)
)

LLchisq(shipley_psem2)
#>   Chisq df P.Value
#> 1 4.143  5   0.529

The above p-value and Chisq stat are consistent with the one found in your book, while

shipley_psem3 <- psem(
  gam(x2 ~ s(x1), data = dat2, family = gaussian),
  glm(x3 ~ x2, data = dat2, family = poisson),
  gam(x4 ~ x2, data = dat2, family = poisson),
  glm(x5 ~ x3 + x4, data = dat2, family = binomial)
)

LLchisq(shipley_psem3)
#>    Chisq     df P.Value
#> 1 19.737 10.291   0.036

These differs, the expected values from your example being :

##   Chisq df P.Value
## 1 3.346  5   0.647

I thus would like your confirmation that the results obtained when using GAMs are still consistent.
Many thanks for your support !