Interpretation of change in fixed effects after including spatial random effect
dario elias
Hello all,
I am working with a logistic regression model.
First I ran the model with only fixed effects, and then I ran it including the spatial autocorrelation as a random effect (SPDE). Some of the fixed effect variables are binary and others are continuous (standardized).
Between both models the fixed effect A varies considerably. In the model without the random variable the mean is 0.026 and the credible interval includes the zero value (-0.608, 0.659). While in the model with random effect the mean is 1.140 and the credible interval does not include the zero value (0.169 , 2.166).
How can one interpret the change in the fixed effect A between both models? Is there a graphic I can make to help in the interpretation?
In the model with random effect, would the coefficient of the fixed effect A indicate the effect of A on the outcome variable when the other fixed effects take the value 0 and there is no spatial autocorrelation?
Thank you for your valuable time
Dario
Model without random effect:
Fixed effects:
mean sd 0.025quant 0.5quant 0.975quant mode kld
Intercept -2.276 0.354 -2.970 -2.276 -1.582 -2.276 0
A 0.026 0.323 -0.608 0.026 0.659 0.026 0
B 0.428 0.117 0.199 0.428 0.656 0.428 0
C 0.936 0.290 0.369 0.936 1.504 0.936 0
D 0.123 0.132 -0.134 0.123 0.381 0.123 0
E -0.155 0.157 -0.462 -0.155 0.152 -0.155 0
F 0.107 0.140 -0.167 0.107 0.382 0.107 0
G 0.086 0.132 -0.172 0.086 0.344 0.086 0
H -0.369 0.260 -0.879 -0.369 0.142 -0.369 0
I 0.017 0.116 -0.211 0.017 0.245 0.017 0
J 0.091 0.117 -0.138 0.091 0.320 0.091 0
K 0.038 0.250 -0.452 0.038 0.527 0.038 0
Deviance Information Criterion (DIC) ...............: 510.81
Deviance Information Criterion (DIC, saturated) ....: 510.81
Effective number of parameters .....................: 11.12
Watanabe-Akaike information criterion (WAIC) ...: 511.34
Effective number of parameters .................: 11.10
Marginal log-Likelihood: -307.52
Model with random effect:
Fixed effects:
mean sd 0.025quant 0.5quant 0.975quant mode kld
Intercept -3.455 0.628 -4.771 -3.428 -2.294 -3.382 0
A 1.140 0.509 0.169 1.131 2.166 1.113 0
B 0.513 0.140 0.241 0.512 0.791 0.510 0
C 0.983 0.344 0.312 0.981 1.662 0.978 0
D 0.121 0.151 -0.177 0.121 0.416 0.122 0
E -0.096 0.192 -0.472 -0.096 0.282 -0.097 0
F 0.073 0.179 -0.278 0.073 0.425 0.073 0
G 0.083 0.181 -0.275 0.084 0.436 0.085 0
H -0.480 0.371 -1.219 -0.477 0.238 -0.470 0
I -0.019 0.144 -0.303 -0.019 0.262 -0.018 0
J 0.141 0.142 -0.136 0.141 0.420 0.140 0
K 0.155 0.293 -0.418 0.154 0.732 0.152 0
Random effects:
Name Model
spatial SPDE2 model
Model hyperparameters:
mean sd 0.025quant 0.5quant 0.975quant mode
Range for spatial.field 6911.26 3009.318 3228.75 6210.92 14731.19 5020.16
Stdev for spatial.field 1.78 0.395 1.15 1.73 2.70 1.63
Deviance Information Criterion (DIC) ...............: 451.33
Deviance Information Criterion (DIC, saturated) ....: 451.33
Effective number of parameters .....................: 54.22
Watanabe-Akaike information criterion (WAIC) ...: 450.50
Effective number of parameters .................: 46.79
Marginal log-Likelihood: -289.02
Finn Lindgren
On 24 May 2023, at 20:00, dario elias <darioezeq...@gmail.com> wrote:
--
You received this message because you are subscribed to the Google Groups "R-inla discussion group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to r-inla-discussion...@googlegroups.com.
To view this discussion on the web, visit https://groups.google.com/d/msgid/r-inla-discussion-group/35a0f7f6-3677-4cb1-be0c-3109dc66d4cdn%40googlegroups.com.
dario elias
Hello Finn, thank you very much for your answer.
I will see the analysis that you suggested.
However, I still don't fully understand how to interpret the coefficient of the fixed effect in the model with the random field.
In both models, the exponential of the coefficient of the variable A would be the odds ratio of A for the response variable, right?
As far as I understand, in logistic regression without the random effect, the exponential of the fixed effect coefficient A indicates the odds ratio of variable A when the other variables have the value 0.
But, how is this coefficient interpreted in logistic regression with the random field? Would the exponential of the coefficient of the fixed effect A indicate the odds ratio of variable A when the other fixed effects take the value 0 and there is no spatial autocorrelation? If not, how is the interpretation?
Again, thank you very much for your time.
Dario
Finn Lindgren
The interpretation most likely would depend on the nature of the
covariate; binary/continuous/geospatial or individual/etc.
If binary, and the model is
E(y|model) = exp(beta_A * A + other + components)
then
E(y|model, A=1) / E(y|model, A=0) = exp(beta_A)
assuming all other components are _unchanged_; they don't need to be zero.
I think that's the odd-ratio type interpretation you describe?
_However_:
If the covariate is inherently _spatial_, then the values of the other
components, in particular any random field, _cannot_ be unchanged,
since they would both depend on location, so this interpretation
doesn't really work.
This is an intrinsic problem with all complex structured models; the
simplistic interpretations from completely independent observation
models don't necessarily work anymore.
What I tend to do is to figure out what well-defined quantity I'm
interested in, and then compute that; this often involves computing
functionals of the model components, and not just the basic parameter
estimates.
E.g. the "intercept" is often not a good representation of the
"spatial average". To get to the actual spatial average, I'd compute
the posterior distribution of the integration average of
exp(predictor) instead.
Finn
Finn Lindgren
email: finn.l...@gmail.com
Helpdesk (Haavard Rue)
You might find this one useful
https://academic.oup.com/jrsssc/article/68/3/543/7058400?login=true
the confounding issue is non-solvable and we have to live with it and
try to get better dealing with it.
> You received this message because you are subscribed to the Google
> Groups "R-inla discussion group" group.
> To unsubscribe from this group and stop receiving emails from it, send
> an email to r-inla-discussion...@googlegroups.com.
> To view this discussion on the web, visit
> https://groups.google.com/d/msgid/r-inla-discussion-group/35a0f7f6-3677-4cb1-be0c-3109dc66d4cdn%40googlegroups.com
> .
--
he...@r-inla.org