EM decreasing in the first few iterations in some instances about iprior HOT 3 CLOSED

In my EM, setting initial values of lambda=0 does not move lambda away from zero!

> mod.iprior <- iprior(stack.loss ~ ., data=stackloss)
START iter 0 -91.76077  
EM complete.

Number of iterations = 2 
Log-likelihood =  -77.99705 
> summary(mod.iprior)

Call:
iprior.formula(formula = stack.loss ~ ., data = stackloss)

RKHS used:
Canonical (Air.Flow, Water.Temp, Acid.Conc.) 

Residuals:
   Min. 1st Qu.  Median 3rd Qu.    Max. 
-10.520  -6.524  -2.524   1.476  24.480 

                Estimate    S.E.    z  P[|Z>z|]    
(Intercept)      17.5238  2.1661 8.09 < 2.2e-16 ***
lam1.Air.Flow     0.0000      NA   NA        NA    
lam2.Water.Temp   0.0000      NA   NA        NA    
lam3.Acid.Conc.   0.0000      NA   NA        NA    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

EM converged to within 0.001 tolerance. No. of iterations: 2
Standard deviation of errors: 9.95 with S.E.: 1.527
T2 statistic: 0 on ??? degrees of freedom.
Log-likelihood value: -77.99705 

I will probably need to explain the EM that I am using. It is an exponential family EM which does not do any real maximisation per se, as the algorithm reduces to an updating sequence of the parameters which has closed form expressions. More on this later...

from iprior.

Just something that I've noticed: the psi parameter is the culprit here. If the starting value for psi is high (say 10) and the true value is lower than the starting value (say 4) then the EM does not decrease at each stage as psi goes from 10 to 4.

On the other hand, if the starting value is lower than the true value (say 0.1) then the EM does decrease for some unknown reason. This need to be looked at further. Maybe the exponential family EM is not suitable in this case.

from iprior.

There was a slight error that also contributed to this. The intercept parameter was not updating properly. This explains why we saw decrease in log-likelihood in the few early EM iterations. As the intercept started to stabilise, there was no decrease in log-likelihood seen. This has been fixed.

from iprior.