Error with test.statistic: the F test is always returned

[luroy]

Hello,
In trying to obtain the p-values associated with each model of the following psem [that is, type 2 Anova, F-test for lm() / type 2 Anova Likelihood ratio (LR) test for glm(..., family = poisson) and for glm.nb() / type 2 Anova, Chisq Wald test for glmer()] :

SEM<-psem(bm_lc_mod1.1<-lm(Tmi ~ 1, data = data),
                 bm_lc_mod1.3<-lm(Tma ~ p1, data = data),
                 bm_lcpwc_mod1.1b<-glm(Rich ~ p1 + Pra1 + Tmi + Tma, family = "poisson", data = data),
                 bm_lcpwc_mod1.2b<-glm.nb(AB ~ Autoc_AB + p2 + Pra2 + p3, data = data),
                 bm_lcpwc_mod1.3<-lm(Co1 ~ p1 + Pra1, data = data),
                 bm_lcpwc_mod1.4b<-lm(Co2 ~ Autoc_Co2 + Pra2, data = data),
                 bm_c_mod1.1q<-glmer(Tx_V~AB+Co1+(1|obs_V), weights=N_V, data = data, family="binomial"),
                 bm_c_mod1.2q<-glmer(Tx_P~Rich+Autoc_Tx_P+(1|obs_P),  weights=N_P, data = data, family="binomial")
)

To do this, I use the coefs() function, as follows:

#test.statistic = "F" for lm()
coefs(
  SEM,
  standardize = "scale",
  standardize.type = "latent.linear",
  test.statistic = "F",
  test.type = "II",
  intercepts = FALSE
) 
#test.statistic = "LR" for glm(, family="poisson) and glm.nb()
coefs(
  SEM,
  standardize = "scale",
  standardize.type = "latent.linear",
  test.statistic = "LR",
  test.type = "II",
  intercepts = FALSE
) 
#test.statistic = "Chisq" for glmer(, family="binomial")
coefs(
  SEM,
  standardize = "scale",
  standardize.type = "latent.linear",
  test.statistic = "Chisq",
  test.type = "II",
  intercepts = FALSE
) 

Unfortunately, the results of these three functions give exactly the same p-values, and these p-values correspond to the default F-test.
Is there any way of obtaining the correct p-values for each model?
Thank you in advance for your help,
Léa