[ADMB Users] difference between ADMB-RE and R/mgcv in SEs for smoother coefficients in a GAM fitted by maximum likelihood
H. Skaug
hskaug at gmail.com
Thu Nov 29 13:10:53 PST 2012
I think there may be a problem with the correlation
between fixed and random effects. I modified Dave's
example a bit to cast it in probabilistic terms where
I know what the covariance matrix should be:
********ADMB program with explanation of hierarchical model:
DATA_SECTION
number y
!! y=10.0;
PARAMETER_SECTION
init_number x
random_effects_vector u(1,1)
objective_function_value f
PROCEDURE_SECTION
f = 0.0;
f -= -0.5*square(x); // Prior on x: x = e1
f -= -0.5*square(u(1)-x); // u|x: u = x + e2
f -= -0.5*square(y-u(1)); // y|u: y = u + e3
// where e1, e2, e3 are all N(0,1)
******* Correlation matrix where the correlation has the wrong sign
D:\tmp\tmp>more simple_variance.cor
The logarithm of the determinant of the hessian = 0.405465
index name value std dev 1
1 x 3.3335e+000 8.1650e-001 1.0000
2 u 6.6668e+000 8.1650e-001 -0.5000 1.0000
Comment: it is counter intuitive that x and u should
be negatively correlated.
***** Calculations in R to find the covarinace matrix
S = matrix(0,3,3,row=c("x","u","y"),col=c("x","u","y"))
S[,]=1
S[2:3,2:3]=2
S[3,3]=3
S12_3 = S[1:2,1:2] - S[1:2,3]%*%solve(S[3,3])%*%S[3,1:2] #
Conditional covariance (x,u) given y
> sqrt(diag(S12_3))
x u
0.8164966 0.8164966
> cov2cor(S12_3)
x u
x 1.0 0.5
u 0.5 1.0
Conclusion: sd's match ADMB, but corrrelation has oposite sign.
Hans
On Thu, Nov 29, 2012 at 6:53 PM, dave fournier <davef at otter-rsch.com> wrote:
> A very simple example shows how the method works.
>
>
> DATA_SECTION
>
> PARAMETER_SECTION
> init_number x
> random_effects_vector u(1,1)
> objective_function_value f
> sdreport_number sd1
> sdreport_number sd2
> PROCEDURE_SECTION
>
> f= square(x-10) + 0.5*square(u(1)) + square(u(1)-x);
> sd1=u(1)-x;
> sd2=x-u(1);
>
>
> The logarithm of the determinant of the hessian = 0.980829
> index name value std.dev 1 2 3
> 1 x 7.5002e+00 6.1237e-01 1.0000
> 2 u 5.0001e+00 5.7735e-01 0.0000 1.0000
> 3 sd1 -2.5001e+00 8.4163e-01 -0.7276 0.6860 1.0000
> 4 sd2 2.5001e+00 8.4163e-01 0.7276 -0.6860 -1.0000 1.0000
>
> I guess the question is whether this is reasonable for sd1. It seems a bit
> large to me.
>
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