How to explain the result of MrsP model

Modeling
1

I fit a Bayesian Multilevel Regression and Poststratification (MrsP) using the data from Chinese General Social Survey. The results are as follows,

	Mean	SD	2.50%	97.50%	n_eff	Rhat
α	-2.071 	1.527 	-5.067 	0.923 	1546 	1.001 
ψ	0.334 	0.177 	-0.024 	0.668 	1394 	1.000 
η	-0.135 	0.079 	-0.296 	0.020 	1690 	0.999 
σ_β	0.096 	0.069 	0.004 	0.257 	1021 	1.006 
σ_γ	0.519 	0.333 	0.181 	1.438 	1043 	1.001 
σ_δ	0.020 	0.031 	0.000 	0.113 	552 	1.005 
σ_ϵ	0.018 	0.029 	0.000 	0.112 	854 	1.006 
σ_ζ	0.305 	0.354 	0.011 	1.202 	1349 	1.001 
β[1]	0.048 	0.111 	-0.131 	0.332 	2584 	1.002 
β[2]	0.022 	0.118 	-0.208 	0.308 	1731 	1.002 
β[3]	0.023 	0.110 	-0.185 	0.294 	3278 	1.000 
β[4]	-0.020 	0.103 	-0.267 	0.179 	2865 	1.001 
β[5]	-0.027 	0.102 	-0.264 	0.159 	3568 	1.000 
β[6]	-0.046 	0.113 	-0.337 	0.135 	2185 	1.002 
β[7]	-0.010 	0.094 	-0.222 	0.186 	2968 	1.000 
β[8]	-0.042 	0.098 	-0.287 	0.125 	2499 	1.001 
β[9]	0.012 	0.091 	-0.164 	0.216 	3911 	1.000 
β[10]	0.000 	0.097 	-0.218 	0.203 	3345 	1.000 
β[11]	0.021 	0.086 	-0.144 	0.224 	2899 	1.001 
β[12]	0.007 	0.093 	-0.193 	0.212 	3108 	1.000 
β[13]	0.009 	0.116 	-0.221 	0.283 	3310 	1.001 
β[14]	0.005 	0.102 	-0.216 	0.238 	2989 	1.000 
β[15]	-0.014 	0.092 	-0.224 	0.172 	2865 	1.001 
β[16]	-0.037 	0.102 	-0.291 	0.139 	2774 	1.001 
β[17]	-0.012 	0.096 	-0.233 	0.188 	3346 	1.000 
β[18]	-0.040 	0.101 	-0.288 	0.128 	2128 	1.003 
β[19]	0.097 	0.128 	-0.065 	0.416 	1267 	1.006 
γ[1]	-0.508 	0.337 	-1.249 	0.044 	1408 	1.000 
γ[2]	-0.030 	0.333 	-0.759 	0.533 	1484 	1.000 
γ[3]	0.142 	0.331 	-0.558 	0.717 	1495 	1.000 
γ[4]	0.190 	0.330 	-0.529 	0.771 	1421 	1.000 
δ[1]	0.005 	0.020 	-0.025 	0.068 	1201 	1.002 
δ[2]	-0.005 	0.020 	-0.068 	0.025 	1198 	1.002 
ϵ[1]	-0.002 	0.017 	-0.044 	0.031 	2388 	0.999 
ϵ[2]	0.002 	0.017 	-0.032 	0.044 	2392 	1.000 
ζ[1]	-0.157 	0.310 	-0.817 	0.217 	1426 	1.001 
ζ[2]	-0.046 	0.296 	-0.626 	0.348 	1576 	1.001 
ζ[3]	0.066 	0.296 	-0.501 	0.522 	1559 	1.001

As are shown in the table. The 95% credible intervals of estimated parameters always cover zero. Are they not statistically significant? Is my model nonsense?
Thank you in advance.

2

Bayesian model reporting typically avoids the language of statistical significance, but it’s possible to make statements that are approximately analogous for practical purposes. Here, we can say that a 95% interval that overlaps zero means that your model and these data collectively lead to less than 97.5% certainty about the sign of the true parameter value.

Unfortunately, this is not something that we can infer from the output you’ve shown. Answering this question generally requires:

  • knowledge of what the model is
  • domain knowledge about the data and process under study, and whether the model (including both its structure and its prior specification) is reasonable
  • usually some form of post-hoc model assessment and criticism, such as posterior predictive checking, to ensure that the model structure still looks reasonable in light of the data
  • often some careful checking to ensure that the model and poststratification implementation are bug-free (i.e. that they actually correspond to the model you intend to estimate)
3 Likes
3

thanks for your reply.