Constructs the control structure for the estimation of the
number of latent factors (r) for use within the glmmPen_FA and
glmm_FA estimation procedures.
Control of Latent Factor Model Number Estimation
Constructs the control structure for the estimation of the
number of latent factors (r) for use within the glmmPen_FA and
glmm_FA estimation procedures.
rControl(
r = NULL,
r_max = NULL,
r_est_method = "GR",
size = 25,
sample = FALSE
)positive integer specifying number of latent common factors to assume
in the model. If NULL (default), this value estimated from the data. See
r_est_method for available estimation procedures, and the Details
section for further details on the general estimation procedure.
If r is specified, the no estimation procedure is performed and the algorithm
uses the input value or r. All other parameters for this function are
relevant for the estimation procedure.
positive integer specifying maximum number of latent factors to consider.
If NULL (default), this value is automatically calculated.
character string indicating method used to estimate number
of latent factors r. Default "GR" uses the Growth Ratio method of
Ahn and Horenstein (2013) (<doi:10.3982/ECTA8968>).
Other available options include "ER" for
the Eigenvalue Ratio method of Ahn and Horenstein (2013) (<doi:10.3982/ECTA8968>)
and "BN1" or "BN2",
the Bai and Ng (2002) method (<dio:10.1111/1468-0262.00273>) using one of two penalties:
(1) (d + p) / (d p) log(d p/(d+p)) or
(2) (d + p) / (d p) log(min(d,p)) where d is the number of groups in
the data and p is the number of total random effect covariates (including the intercept)
positive integer specifying the total number of pseudo random
effect estimates to use in the estimation procedure for the number of latent factors
r, which is restricted to be no less than 25. If this size is greater
than the number of groups in the data (i.e.~the number of levels of the grouping
variable), then a sampling procedure is used to increase the number of pseudo estimates
to the value of size if the value of sample is TRUE.
logical value indicating if the total number of pseudo random effect
estimates to use in the estimation procedure for the number of latent common factors r
should be larger than the number of unique groups in the data, where the number
of pseudo estimates are increased to the value of size using a sampling
procedure. Default is FALSE. If TRUE, the sampling procedure is only
performed if the value of size is greater than the number of groups in the data.
Estimation of r procedure: For each level of the group variable separately,
we identify the observations within that group and
fit a regular penalized generalized linear model where the penalty value is the
minimum fixed effect penalty. These group-specific estimates, which we label as 'pseudo random effects',
are placed into a matrix G
(rows = number of levels of the grouping variable, columns = number of random effect covariates),
and this pseudo random effects matrix is treated as the observed outcome matrix used in
the "GR", "ER", and "BN" estimation procedures described above in the description of r_est_method.