Hi R-users,

 

I am trying to estimate function parameters using optim(). My count
observations follows a Poisson like distribution. The problem is that I
wanna express the lambda coefficient, in the passion likelihood
function, as a linear function of other covariates (and thus of other
coefficients). The codes that I am using (except data frame) are the
following (FYI the parameters need to be positive):

 

myfun <- function(coeff, H1, H2, p, Range)

{

 
(coeff[1]+coeff[2]*H1+coeff[3]*H2+coeff[4]*p+H1*Range*coeff[5]+H2*Range*
coeff[6]+H1*H2*coeff[7])*exp((coeff[8]+coeff[9]*H1+coeff[10]*H2+coeff[11
]*p+H1*Range*coeff[12]+H2*Range*coeff[13]+H1*H2*coeff[14])*(Range-1))+co
eff[15]+coeff[16]*H1+coeff[17]*H2+coeff[18]*p+H1*Range*coeff[19]+H2*Rang
e*coeff[20]+H1*H2*coeff[21]

}

 

SS <- function(coeff,Range,H1,H2,p,steps)

{

sum((steps - myfun(coeff,Range,H1,H2,p))^2)

}

 

coeff <-
c(0.1,0.1,0.1,0.1,0.1,1,5,5,5,1,1,1,1,1,1,1,0.1,0.1,0.1,0.1,0.1)

scale <-
c(0.1,0.1,0.1,0.1,0.1,1,5,5,5,1,1,1,1,1,1,1,0.1,0.1,0.1,0.1,0.1)

 

est_coeff <- optim(par=coeff, fn = SS, H1=org_results$H1,
H2=org_results$H2, p=org_results$p, Range=org_results$Range,
steps=org_results$no.steps, method= 'L-BFGS-B', lower = rep(0, 21),
upper = rep(Inf, 21), control = list(trace=FALSE, parscale=scale),
hessian=TRUE)

 

this is the output:

 

$par

 [1]  0.099794607  0.099841098  0.099896127  0.099899549  0.099856776
0.991269412  4.807153280

 [8] 25.115556187 55.961674737  1.519658195  1.378913148  2.800328223
1.448902455  2.280837645

[15]  1.594648898  0.011581676  0.040651369  0.000000000  0.000000000
0.000000000  0.002717246

 

$value

[1] 14535187

 

$counts

function gradient 

      54       54 

 

$convergence

[1] 0

 

$message

[1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"

 

$hessian

               [,1]          [,2]          [,3]          [,4]
[,5]          [,6]

 [1,]  0.000000e+00  0.000000e+00  0.000000e+00 -0.0023283064
0.0000000000  2.328306e-03

 [2,]  0.000000e+00  0.000000e+00  0.000000e+00 -0.0023283064
0.0000000000  2.328306e-03

 [3,]  0.000000e+00  0.000000e+00  0.000000e+00  0.0023283064
0.0000000000  0.000000e+00

 [4,] -2.328306e-03 -2.328306e-03  2.328306e-03  0.0000000000
-0.0023283064  2.328306e-04

 [5,]  0.000000e+00  0.000000e+00  0.000000e+00 -0.0023283064
0.0046566129 -2.095476e-03

 [6,]  2.328306e-03  2.328306e-03  0.000000e+00  0.0002328306
-0.0020954758  0.000000e+00

 [7,]  9.313226e-05  9.313226e-05  4.656613e-05  0.0023748726
0.0001396984  4.656613e-05

 [8,] -4.284550e-01 -4.284550e-01 -1.916196e-01 -0.2018641680
-0.3814231604 -1.689885e-01

 [9,] -4.284550e-01 -4.284550e-01 -1.916196e-01 -0.2018641680
-0.3814231604 -1.689885e-01

[10,] -1.892913e-01 -1.892913e-01 -1.240987e-01 -0.0880099833
-0.1706648618 -1.098961e-01

[11,] -1.974404e-01 -1.974404e-01 -8.568168e-02 -0.1315493137
-0.1781154424 -7.823110e-02

[12,] -3.885943e-01 -3.885943e-01 -1.704320e-01 -0.1802109182
-0.3480818123 -1.513399e-01

[13,] -1.706649e-01 -1.706649e-01 -1.108274e-01 -0.0789295882
-0.1504085958 -9.872019e-02

[14,] -1.892913e-01 -1.892913e-01 -1.240987e-01 -0.0880099833
-0.1706648618 -1.098961e-01

[15,]  2.813991e+00  2.813991e+00  1.214910e+00  1.3138633221
2.5336630642  1.093373e+00

[16,]  2.814224e+00  2.814224e+00  1.212582e+00  1.3138633221
2.5336630642  1.093373e+00

[17,]  1.213048e+00  1.213048e+00  7.892959e-01  0.5634501576
1.0943040252  7.092021e-01

[18,]  1.317821e+00  1.317821e+00  5.704351e-01  0.8870847523
1.1851079762  5.112961e-01

[19,]  2.537854e+00  2.537854e+00  1.089647e+00  1.1827796698
2.2817403078  9.855721e-01

[20,]  1.094304e+00  1.094304e+00  7.101335e-01  0.5122274160
0.9802170098  6.388873e-01

[21,]  1.215376e+00  1.215376e+00  7.939525e-01  0.5657784641
1.0919757187  7.094350e-01

               [,7]        [,8]        [,9]       [,10]       [,11]
[,12]       [,13]

 [1,]  9.313226e-05 -0.42845495 -0.42845495 -0.18929131 -0.19744039
-0.38859434 -0.17066486

 [2,]  9.313226e-05 -0.42845495 -0.42845495 -0.18929131 -0.19744039
-0.38859434 -0.17066486

 [3,]  4.656613e-05 -0.19161962 -0.19161962 -0.12409873 -0.08568168
-0.17043203 -0.11082739

 [4,]  2.374873e-03 -0.20186417 -0.20186417 -0.08800998 -0.13154931
-0.18021092 -0.07892959

 [5,]  1.396984e-04 -0.38142316 -0.38142316 -0.17066486 -0.17811544
-0.34808181 -0.15040860

 [6,]  4.656613e-05 -0.16898848 -0.16898848 -0.10989606 -0.07823110
-0.15133992 -0.09872019

 [7,]  9.313226e-05 -0.18775463 -0.18775463 -0.12246892 -0.08759089
-0.16880222 -0.11008233

 [8,] -1.877546e-01  0.12330711  0.12330711  0.07711351  0.05806796
0.11092052  0.06952323

 [9,] -1.877546e-01  0.12330711  0.12330711  0.07711351  0.05806796
0.11092052  0.06952323

[10,] -1.224689e-01  0.07711351  0.07711351  0.05681068  0.03585592
0.06938353  0.05122274

[11,] -8.759089e-02  0.05806796  0.05806796  0.03585592  0.03864989
0.05215406  0.03213063

[12,] -1.688022e-01  0.11092052  0.11092052  0.06938353  0.05215406
0.09965152  0.06286427

[13,] -1.100823e-01  0.06952323  0.06952323  0.05122274  0.03213063
0.06286427  0.04656613

[14,] -1.224689e-01  0.07711351  0.07711351  0.05681068  0.03585592
0.06938353  0.05122274

[15,]  1.214491e+00 -0.79902820 -0.79902820 -0.49918890 -0.37578866
-0.71944669 -0.44936314

[16,]  1.214491e+00 -0.79898164 -0.79898164 -0.49918890 -0.37602149
-0.71921386 -0.44936314

[17,]  7.884577e-01 -0.49867667 -0.49867667 -0.36740676 -0.23562461
-0.45029446 -0.32992102

[18,]  5.675014e-01 -0.37644058 -0.37644058 -0.23585744 -0.25262125
-0.33900142 -0.20791776

[19,]  1.091324e+00 -0.71818940 -0.71818940 -0.45052730 -0.33900142
-0.64703636 -0.40209852

[20,]  7.117167e-01 -0.45038760 -0.45038760 -0.32759272 -0.21001324
-0.40465966 -0.29732473

[21,]  7.907860e-01 -0.49867667 -0.49867667 -0.36740676 -0.23562461
-0.45029446 -0.33038668

            [,14]         [,15]         [,16]         [,17]
[,18]         [,19]

 [1,] -0.18929131  2.813991e+00  2.814224e+00  1.213048e+00
1.317821e+00  2.537854e+00

 [2,] -0.18929131  2.813991e+00  2.814224e+00  1.213048e+00
1.317821e+00  2.537854e+00

 [3,] -0.12409873  1.214910e+00  1.212582e+00  7.892959e-01
5.704351e-01  1.089647e+00

 [4,] -0.08800998  1.313863e+00  1.313863e+00  5.634502e-01
8.870848e-01  1.182780e+00

 [5,] -0.17066486  2.533663e+00  2.533663e+00  1.094304e+00
1.185108e+00  2.281740e+00

 [6,] -0.10989606  1.093373e+00  1.093373e+00  7.092021e-01
5.112961e-01  9.855721e-01

 [7,] -0.12246892  1.214491e+00  1.214491e+00  7.884577e-01
5.675014e-01  1.091324e+00

 [8,]  0.07711351 -7.990282e-01 -7.989816e-01 -4.986767e-01
-3.764406e-01 -7.181894e-01

 [9,]  0.07711351 -7.990282e-01 -7.989816e-01 -4.986767e-01
-3.764406e-01 -7.181894e-01

[10,]  0.05681068 -4.991889e-01 -4.991889e-01 -3.674068e-01
-2.358574e-01 -4.505273e-01

[11,]  0.03585592 -3.757887e-01 -3.760215e-01 -2.356246e-01
-2.526212e-01 -3.390014e-01

[12,]  0.06938353 -7.194467e-01 -7.192139e-01 -4.502945e-01
-3.390014e-01 -6.470364e-01

[13,]  0.05122274 -4.493631e-01 -4.493631e-01 -3.299210e-01
-2.079178e-01 -4.020985e-01

[14,]  0.05681068 -4.991889e-01 -4.991889e-01 -3.674068e-01
-2.358574e-01 -4.505273e-01

[15,] -0.49918890  1.312200e+06  2.638980e+07  6.298560e+05
6.298560e+05  1.319490e+07

[16,] -0.49918890  2.638980e+07  7.437258e+08  1.266710e+07
1.266710e+07  3.718629e+08

[17,] -0.36740676  6.298560e+05  1.266710e+07  4.283021e+05
3.023309e+05  6.333552e+06

[18,] -0.23585744  6.298560e+05  1.266710e+07  3.023309e+05
4.283021e+05  6.333552e+06

[19,] -0.45052730  1.319490e+07  3.718629e+08  6.333552e+06
6.333552e+06  2.355132e+08

[20,] -0.32759272  3.149280e+05  6.333552e+06  2.141510e+05
1.511654e+05  4.011250e+06

[21,] -0.36740676  1.266710e+07  3.569884e+08  8.613631e+06
6.080210e+06  1.784942e+08

              [,20]         [,21]

 [1,]  1.094304e+00  1.215376e+00

 [2,]  1.094304e+00  1.215376e+00

 [3,]  7.101335e-01  7.939525e-01

 [4,]  5.122274e-01  5.657785e-01

 [5,]  9.802170e-01  1.091976e+00

 [6,]  6.388873e-01  7.094350e-01

 [7,]  7.117167e-01  7.907860e-01

 [8,] -4.503876e-01 -4.986767e-01

 [9,] -4.503876e-01 -4.986767e-01

[10,] -3.275927e-01 -3.674068e-01

[11,] -2.100132e-01 -2.356246e-01

[12,] -4.046597e-01 -4.502945e-01

[13,] -2.973247e-01 -3.303867e-01

[14,] -3.275927e-01 -3.674068e-01

[15,]  3.149280e+05  1.266710e+07

[16,]  6.333552e+06  3.569884e+08

[17,]  2.141510e+05  8.613631e+06

[18,]  1.511654e+05  6.080210e+06

[19,]  4.011250e+06  1.784942e+08

[20,]  1.356290e+05  4.306815e+06

[21,]  4.306815e+06  2.427521e+08

 

 

What does the message about convergence mean? (I thought it was
something related to parameter scaling issues. That is why I provided a
'parscale' argument)

 

Also when trying to calculate SE, I got the following messages:

 

> OI<-solve(est_coeff$hessian)

Error in solve.default(est_coeff$hessian) : 

  Lapack routine dgesv: system is exactly singular

> se<-sqrt(diag(OI))

Warning message:

In sqrt(diag(OI)) : NaNs produced

> 

 

I would appreciate it very much any suggestion you might give

 

Thanks for your help

 

Lorenzo


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