分段 SEM 中的零膨胀模型

Question

I analyze bee observations from a field experiment and I want to apply SEM. Piecewise sem (psem) seems most appropriate. My problem is that my data is highly zero-inflated because of many observations with zero bees. So far, I worked with glmmTMB and nbinom2-distribution in the analysis, which worked very well. Unfortunately, glmmTMB and nbinom2 are not implemented in psem and I am now clueless whether and how I can apply psem to my data.

By means of the piecewise sem, I want to investigate the effect of the treatment (which is flower strip, hedgerow …) on flower abundance (which I want to be log-transformed because of strongly varying counts) and plant species richness and finally on the abundance of bees by taking into account the month and the year. This way, I want to quantify the contribution of the vegetation variables and the direct effects of the treatments and hope to find an indication about whether the treatments differ also in other properties than only flower abundance and plant species richness.

The psem-models include several dummy variables for the treatments (FF, HC, HI) and the months of observation. w_b_abu indicates the aubndance of bees, pl_abu the abundance of flowers (pl_abu_ln = log-tranformed) and pl_sr the plant species richness.

My code is the following:

w_b_abu_sem <- psem(
  glmer(w_b_abu  ~ FF + HC + HI + pl_abu_ln + pl_sr + april + may + june + july + august + september + years + (1|site), dat_treat_habitat, family = "poisson"),
  lmer(pl_abu_ln  ~ FF + HC + HI + april + may + june + july + august + september  + years +  (1|site),  dat_treat_habitat),
  glmer(pl_sr  ~ FF + HC + HI + pl_abu_ln + april + may + june + july + august + september  + years + >  (1|site), dat_treat_habitat, family = "poisson"),
  dat_treat_habitat)

This SEM however fails to converge with "Model failed to converge with max|grad| =..." (because of submodels 1 and 3). Anyway, the poisson error distribution does not really fit the data. I used “nbinom2” in the previous analysis, which worked much better, but is not implemented in psem. Submodel 1 is highly zero-inflated (tested with Dharma).

My question is, whether there are possibilities to include zero-inflated models with nbinom2-distribution in psem.

If not, do you have other ideas how I could apply psem on my data? An idea that I had was to transform the variables to make them normally distributed. Would that be appropriate? And if so, which way of transformation would be best?

To try out the psem I scaled the responses, so that they are “normally distributed” (they are not indeed). This psem version works, but I fear that it violates several statistical assumptions:

w_b_abu_sem <- psem(
  lmer(w_b_abu_scaled  ~ FF + HC + HI + pl_abu_ln + pl_sr_scaled + april + may + june + july + august + september + years + (1|site), dat_treat_habitat),
  lmer(pl_abu_ln  ~ FF + HC + HI + april + may + june + july + august + september  + years +  (1|site), dat_treat_habitat),
  lmer(pl_sr_scaled  ~ FF + HC + HI + pl_abu_ln + april + may + june + july + august + september  + years + (1|site), dat_treat_habitat),
  dat_treat_habitat)

This is the head of my data.table:

  w_b_abu pl_abu pl_abu_ln pl_sr FF HC HI april may june july august september years
1       0    730  6.593045     2  0  1  0     1   0    0    0      0         0     0
2       3     51  3.931826     4  0  1  0     1   0    0    0      0         0     0
3       3     41  3.713572     3  0  1  0     1   0    0    0      0         0     0
4       0     43  3.761200     4  0  1  0     1   0    0    0      0         0     0
5       4    126  4.836282     3  0  1  0     0   1    0    0      0         0     0
6       0      0  0.000000     0  0  1  0     0   0    1    0      0         0     0

I would really appreciate help – thank you very much in advance. This is the first time I ask a question here and I hope I don't miss something. I can also upload the full dataset if necessary.

Answer 1

I got the model running without glmmTMB. It works this way (without zero-inflation):

w_b_abu_sem <- psem( glmer.nb(w_b_abu ~ FF + HC + HI + pl_abu_ln + pl_sr + april + may + june + july + august + september + years + (1|site), dat_treat_habitat, control=glmerControl(optimizer="bobyqa"), nAGQ=0), lmer(pl_abu_ln ~ FF + HC + HI + april + may + june + july + august + september + years + (1|site), dat_treat_habitat), glmer(pl_sr ~ FF + HC + HI + pl_abu_ln + april + may + june + july + august + september + years + (1|site), dat_treat_habitat, family = "poisson", control=glmerControl(optimizer="bobyqa"), nAGQ=0), dat_treat_habitat)