Fisher_info.RdCalculates the expected, observed, or average Fisher information matrix from a fitted linear mixed effects model (lmeStruct object) or generalized least squares model (glsStruct object).
Fisher_info(mod, type = "expected", separate_variances = FALSE)Fitted model of class lmeStruct or glsStruct.
Type of information matrix. One of "expected" (the
default), "observed", or "average".
Logical indicating whether to return the Fisher
information matrix for separate level-1 variance components if using
varIdent function to allow for different variances per stratum.
Default is FALSE.
Information matrix corresponding to variance component parameters of
mod.
If separate_variances = TRUE and if weights = varIdent(form =
~ 1 | Stratum) is specified in the model fitting, the Fisher information
matrix for separate level-1 variance estimates will be returned. If
separate_variances = TRUE but if the weighting structure is not
specified with varIdent, or if separate_variances = FALSE,
then the Fisher information matrix for the default variance components will
be returned.
library(nlme)
data(Bryant2016)
Bryant2016_RML <- lme(fixed = outcome ~ treatment,
random = ~ 1 | school/case,
correlation = corAR1(0, ~ session | school/case),
data = Bryant2016)
Fisher_info(Bryant2016_RML, type = "expected")
#> Tau.school.var((Intercept))
#> Tau.school.var((Intercept)) 1.322701e-05
#> Tau.case.var((Intercept)) 3.481280e-06
#> cor_params 4.031958e-02
#> sigma_sq 2.034762e-06
#> Tau.case.var((Intercept)) cor_params
#> Tau.school.var((Intercept)) 3.481280e-06 4.031958e-02
#> Tau.case.var((Intercept)) 1.299375e-05 1.510332e-01
#> cor_params 1.510332e-01 2.744557e+05
#> sigma_sq 7.536166e-06 -5.762687e+00
#> sigma_sq
#> Tau.school.var((Intercept)) 2.034762e-06
#> Tau.case.var((Intercept)) 7.536166e-06
#> cor_params -5.762687e+00
#> sigma_sq 1.320509e-04
Fisher_info(Bryant2016_RML, type = "average")
#> Tau.school.var((Intercept))
#> Tau.school.var((Intercept)) 1.528840e-05
#> Tau.case.var((Intercept)) 3.168824e-06
#> cor_params 3.814212e-02
#> sigma_sq 1.829061e-06
#> Tau.case.var((Intercept)) cor_params
#> Tau.school.var((Intercept)) 3.168824e-06 3.814212e-02
#> Tau.case.var((Intercept)) 4.508868e-06 5.930354e-02
#> cor_params 5.930354e-02 2.673951e+05
#> sigma_sq 2.619958e-06 -5.762462e+00
#> sigma_sq
#> Tau.school.var((Intercept)) 1.829061e-06
#> Tau.case.var((Intercept)) 2.619958e-06
#> cor_params -5.762462e+00
#> sigma_sq 1.320715e-04
Bryant2016_RML2 <- lme(fixed = outcome ~ treatment,
random = ~ 1 | school/case,
correlation = corAR1(0, ~ session | school/case),
weights = varIdent(form = ~ 1 | treatment),
data = Bryant2016)
Fisher_info(Bryant2016_RML2, separate_variances = TRUE)
#> Tau.school.var((Intercept))
#> Tau.school.var((Intercept)) 1.354534e-05
#> Tau.case.var((Intercept)) 3.853874e-06
#> cor_params 5.241303e-03
#> sigma_sq.baseline 3.192872e-06
#> sigma_sq.treatment -6.827965e-07
#> Tau.case.var((Intercept)) cor_params
#> Tau.school.var((Intercept)) 3.853874e-06 5.241303e-03
#> Tau.case.var((Intercept)) 3.162009e-05 7.733113e-02
#> cor_params 7.733113e-02 2.115804e+05
#> sigma_sq.baseline 2.369386e-05 -2.095870e+00
#> sigma_sq.treatment -3.501822e-06 -3.798230e+00
#> sigma_sq.baseline sigma_sq.treatment
#> Tau.school.var((Intercept)) 3.192872e-06 -6.827965e-07
#> Tau.case.var((Intercept)) 2.369386e-05 -3.501822e-06
#> cor_params -2.095870e+00 -3.798230e+00
#> sigma_sq.baseline 1.319001e-04 -2.810345e-05
#> sigma_sq.treatment -2.810345e-05 1.190946e-04