Discrepancy in negbin estimates and conditional effects plot

General
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1

Hi all,

I have a discrepancy between the model results and the conditional effect plot. I may not be interpreting the results of my negbinomial model correctly.

The model seems to show a higher difference from the intercept in phase M18, while the conditional effects show a decrease from M6 and M12.

Can anyone help me to understand what is happening?

Thanks in advance!

summary(model_mc_param)
 Family: negbinomial 
  Links: mu = log; shape = identity 
Formula: mc_total_parameters ~ phase + offset(log_glosses) + (1 + phase | id) + (1 + phase | exercise) 
   Data: data (Number of observations: 1245) 
  Draws: 4 chains, each with iter = 6000; warmup = 2000; thin = 1;
         total post-warmup draws = 16000

Multilevel Hyperparameters:
~exercise (Number of levels: 36) 
                        Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)               0.36      0.06     0.26     0.49 1.00     4703     8552
sd(phaseM12)                0.07      0.06     0.00     0.22 1.00     7424     7358
sd(phaseM18)                0.12      0.09     0.01     0.33 1.00     3835     6222
sd(phaseM24)                0.09      0.07     0.00     0.24 1.00     4332     5602
cor(Intercept,phaseM12)     0.03      0.36    -0.67     0.71 1.00    15314    10652
cor(Intercept,phaseM18)     0.14      0.34    -0.55     0.74 1.00    13570    10639
cor(phaseM12,phaseM18)      0.03      0.38    -0.69     0.72 1.00     8962    11468
cor(Intercept,phaseM24)    -0.22      0.36    -0.80     0.56 1.00    11032    11319
cor(phaseM12,phaseM24)      0.05      0.38    -0.69     0.73 1.00    11533    12285
cor(phaseM18,phaseM24)      0.00      0.37    -0.70     0.70 1.00    11369    12232

~id (Number of levels: 14) 
                        Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)               0.36      0.09     0.22     0.57 1.00     4699     7111
sd(phaseM12)                0.16      0.10     0.01     0.38 1.00     4148     5204
sd(phaseM18)                0.11      0.08     0.00     0.31 1.00     4590     6101
sd(phaseM24)                0.50      0.13     0.30     0.80 1.00     6468     9603
cor(Intercept,phaseM12)    -0.25      0.33    -0.79     0.48 1.00    12117    11335
cor(Intercept,phaseM18)    -0.05      0.36    -0.70     0.65 1.00    14336    11928
cor(phaseM12,phaseM18)      0.02      0.37    -0.69     0.71 1.00    11878    11841
cor(Intercept,phaseM24)    -0.22      0.25    -0.65     0.30 1.00     8296    10446
cor(phaseM12,phaseM24)      0.20      0.33    -0.50     0.75 1.00     3356     5775
cor(phaseM18,phaseM24)     -0.09      0.35    -0.73     0.60 1.00     3580     7045

Regression Coefficients:
          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept    -1.02      0.13    -1.27    -0.75 1.00     3878     5836
phaseM12     -0.16      0.10    -0.34     0.03 1.00    10325    10434
phaseM18     -0.33      0.09    -0.52    -0.15 1.00    11311    10870
phaseM24     -0.24      0.15    -0.56     0.06 1.00     7703     9414

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
shape     3.57      0.43     2.84     4.52 1.00    14575    11398

Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

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2

Hi,
The plot seems to correspond perfectly to the estimates in your print from R (section on regression coefficients). M6 = exp(intercept), M12 = exp(intercept + phaseM12), M18 = exp(intercept + phaseM18), etc. I’m not sure about the the exact values on the y axis of your plot (e.g., for M6: exp(-1) is not ~2.5), but the relative differences make sense.

3

Thank you for your quick answer! I was also wondering what are the numbers of y. With the model I am trying to analyse the count of errors made by participant across different phases. I am expecting a decreasing trend, but I suppose I cannot interpret correctly the estimates.

What should the y axis of the conditional effects plot show in this case? The probabilities or the counts of errors?

Thank you!