#' Black White Visual Impairment data set
#'
#' Visual impairment dataset acquired from
#' supplementary materials of https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4203426/
#'
#' References
#'
#' - Tielsch JM, Sommer A, Katz J, Quigley H, Ezrine S. Socioeconomic status and visual impairment among urban Americans. Archives of ophthalmology. 1991;109:637–641.
#'
#' - Liang KY, Zeger SL. Longitudinal data analysis using generalized linear models. Biometrika. 1986;73:13–22.
#'
#' - Swihart, B. J., Caffo, B. S. and Crainiceanu, C. M. (2014) A unifying framework for marginalised random-476
#' intercept models of correlated binary outcomes. International Statistical Review, 82, 275–295
#'
#' @format A data frame with 10398 rows and 4 variables for 5199 unique patients:
#' \describe{
#' \item{id}{subject id}
#' \item{black}{1 if subject was black; 0 if white}
#' \item{variable}{eye1 for left eye, eye2 for right eye}
#' \item{value}{1 if the eye is impaired, 0 if healthy}
#' }
#' @source \url{https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4203426/}
#' @examples
#' \donttest{
#' ## Example 3.5 from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4203426/
#' attach(bwVI)
#' head(bwVI)
#' o.value <- value ## lesson learned! got an error when I used "value"
#' (LLB <-
#' gnlrim::gnlrim(y=cbind(o.value, 1-o.value),
#' mu = ~ plogis(Intercept + black*b_p + rand1),
#' pmu = c(Intercept = -4.88, b_p=0.134),
#' pmix=c(var=2.03),
#' p_uppb = c( 50, 9, 20.00),
#' p_lowb = c( -50, -9, 0.05),
#' distribution="binomial",
#' nest=id,
#' random=c("rand1"),
#' mixture="logit-bridge-var",
#' ooo=TRUE,
#' compute_hessian = FALSE,
#' compute_kkt = FALSE,
#' trace=1,
#' method='nlminb',
#' )
#' )
#' # > head(bwVI)
#' # id black variable value
#' # 1 1 1 eye1 1
#' # 2 1 1 eye2 1
#' # 3 2 1 eye1 1
#' # 4 2 1 eye2 1
#' # 5 3 1 eye1 1
#' # 6 3 1 eye2 1
#' # > o.value <- value ## lesson learned! got an error when I used "value"
#' # > (LLB <-
#' # + gnlrim::gnlrim(y=cbind(o.value, 1-o.value),
#' # + mu = ~ plogis(Intercept + black*b_p + rand1),
#' # + pmu = c(Intercept = -4.88, b_p=0.134),
#' # + pmix=c(var=2.03),
#' # + p_uppb = c( 50, 9, 20.00),
#' # + p_lowb = c( -50, -9, 0.05),
#' # + distribution="binomial",
#' # + nest=id,
#' # + random=c("rand1"),
#' # + mixture="logit-bridge-var",
#' # + ooo=TRUE,
#' # + compute_hessian = FALSE,
#' # + compute_kkt = FALSE,
#' # + trace=1,
#' # + method='nlminb',
#' # + )
#' # + )
#' # [1] 3
#' # Intercept b_p var
#' # -4.880 0.134 2.030
#' # [1] 3119.63
#' # fn is fn
#' # Looking for method = nlminb
#' # Function has 3 arguments
#' # par[ 1 ]: -50 <? -4.88 <? 50 In Bounds
#' # par[ 2 ]: -9 <? 0.134 <? 9 In Bounds
#' # par[ 3 ]: 0.05 <? 2.03 <? 20 In Bounds
#' # Analytic gradient not made available.
#' # Analytic Hessian not made available.
#' # Scale check -- log parameter ratio= 1.561315 log bounds ratio= 0.7447275
#' # Method: nlminb
#' # 0: 3119.6299: -4.88000 0.134000 2.03000
#' # 1: 2791.2694: -4.06317 0.507976 2.46924
#' # 2: 2743.1744: -3.16525 0.142932 2.71519
#' # 3: 2729.2153: -3.48196 -0.400397 3.49268
#' # 4: 2710.6152: -3.83306 0.175929 4.23063
#' # 5: 2709.7961: -3.77051 0.184101 4.28020
#' # 6: 2709.2022: -3.80107 0.130731 4.33171
#' # 7: 2708.0638: -3.76409 0.123961 4.48770
#' # 8: 2702.5219: -3.97565 0.0273767 5.52687
#' # 9: 2700.4295: -4.24106 0.170311 6.49712
#' # 10: 2700.0148: -4.28328 0.109940 6.91920
#' # 11: 2699.9724: -4.30180 0.104920 7.08190
#' # 12: 2699.9702: -4.30653 0.106829 7.11938
#' # 13: 2699.9701: -4.30680 0.107369 7.12115
#' # 14: 2699.9701: -4.30677 0.107430 7.12092
#' # Post processing for method nlminb
#' # Successful convergence!
#' # Save results from method nlminb
#' # $par
#' # Intercept b_p var
#' # -4.3067653 0.1074302 7.1209235
#' #
#' # $message
#' # [1] "relative convergence (4)"
#' #
#' # $convcode
#' # [1] 0
#' #
#' # $value
#' # [1] 2699.97
#' #
#' # $fevals
#' # function
#' # 18
#' #
#' # $gevals
#' # gradient
#' # 51
#' #
#' # $nitns
#' # [1] 14
#' #
#' # $kkt1
#' # [1] NA
#' #
#' # $kkt2
#' # [1] NA
#' #
#' # $xtimes
#' # user.self
#' # 752.63
#' #
#' # Assemble the answers
#' # Intercept b_p var value fevals gevals niter convcode kkt1
#' # nlminb -4.306765 0.1074302 7.120923 2699.97 18 51 14 0 NA
#' # kkt2 xtime
#' # nlminb NA 752.63
#'
#' }
"bwVI"
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