R/calc_collin_diag.R
In emilelatour/lamisc: Latour's Little Helpers
Defines functions
calc_collin_diag
Documented in
calc_collin_diag
#' Calculate Collinearity Diagnostics
#'
#' This function computes collinearity diagnostics, including variance inflation factors (VIF), tolerance, R-squared values, eigenvalues, condition indices, and more. It replicates functionality similar to what is described in the [Stata collinearity diagnostics page](http://www.philender.com/courses/categorical/notes2/collin.html).
#'
#' @param data A data frame containing the variables to analyze.
#' @param ... Variables to include in the analysis, specified without quotes.
#' @param method The method for calculating the correlation matrix. Default is `"pearson"`.
#' @param use How to handle missing values when calculating correlations. Default is `"complete.obs"`.
#' @param method_for_eigen Specifies the method for calculating eigenvalues and condition indices. Options are `"corr"` for the correlation matrix or `"sscp"` for the scaled sum of squares and cross-product matrix. Default is `"corr"`.
#' @param show_inv_cor_mat Logical. If `TRUE`, includes the inverse correlation matrix in the output. Default is `FALSE`.
#'
#' @return A list with the following components:
#' \item{table}{A tibble with the collinearity diagnostics for each variable. Includes VIF, tolerance, R-squared, eigenvalues, and condition indices.}
#' \item{summary}{A tibble summarizing the mean VIF, condition number, and determinant of the correlation matrix.}
#' \item{inv_cor_mat}{The inverse correlation matrix, if `show_inv_cor_mat = TRUE`.}
#'
#' @examples
#' # Example data
#' library(dplyr)
#' # Examples from Phil Ender
#' # http://www.philender.com/courses/categorical/notes2/collin.html
#'
#' hsbdemo <- read.csv("https://stats.idre.ucla.edu/stat/data/hsbdemo.csv")
#' dplyr::glimpse(hsbdemo)
#'
#' calc_collin_diag(data = hsbdemo,
#' female,
#' schtyp,
#' read,
#' write,
#' math,
#' science,
#' socst,
#' method_for_eigen = "corr",
#' method = "pearson")
#'
#'
#' set.seed(123) # Ensure reproducibility
#'
#' n <- 100 # Number of rows
#'
#' lahigh <- tibble(
#' id = 1000 + seq_len(n),
#' gender = sample(c("male", "female"), n, replace = TRUE),
#' ethnic = sample(c("hispanic", "filipino", "afr-amer", "asian", "white"), n, replace = TRUE),
#' school = sample(1:2, n, replace = TRUE),
#' algebra = sample(0:4, n, replace = TRUE),
#' math = sample(0:4, n, replace = TRUE),
#' eng95 = sample(0:4, n, replace = TRUE),
#' eng94 = sample(0:4, n, replace = TRUE),
#' mathnce = runif(n, 1, 100), # Continuous values between 1 and 100
#' langnce = runif(n, 1, 100),
#' mathpr = sample(1:100, n, replace = TRUE), # Integer percentiles
#' langpr = sample(1:100, n, replace = TRUE),
#' biling = sample(0:3, n, replace = TRUE),
#' engprof = sample(0:4, n, replace = TRUE),
#' daysatt = sample(40:90, n, replace = TRUE),
#' daysabs = sample(0:35, n, replace = TRUE)
#' )
#'
#' dplyr::glimpse(lahigh)
#'
#' calc_collin_diag(data = lahigh,
#' mathnce,
#' langnce,
#' mathpr,
#' langpr,
#' method_for_eigen = "corr",
#' method = "pearson")
#'
#' calc_collin_diag(data = lahigh,
#' mathnce,
#' langnce,
#' method_for_eigen = "corr",
#' method = "pearson")
#'
#' @export
#'
#'
calc_collin_diag <- function(data,
...,
method = "pearson",
use = "complete.obs",
method_for_eigen = "corr",
show_inv_cor_mat = FALSE) {
# Fix no visible binding for global variable
variable <- predictors <- form <- r_squared <- vif <- sqrt_vif <- tolerance <- eigenval <- rnk <- cond_index <- NULL
# vars <- rlang::enquos(...)
#### Make sure that all variables are numeric --------------------------------
# data <- data %>%
# dplyr::select(!!! vars) %>%
# mutate_all(.tbl = .,
# .funs = list(~ as.numeric(.)))
data <- data %>%
dplyr::select(...) %>%
mutate(dplyr::across(.cols = dplyr::everything(),
.fns = ~ make_numeric(.)))
vars_names <- names(data)
#### Rsqrd, vif, tolerance --------------------------------
res <- tibble::tibble(
variable = vars_names
) %>%
mutate(predictors = purrr::map(.x = variable,
.f = ~ vars_names[!vars_names %in% .x]),
form = purrr::map2_chr(.x = variable,
.y = predictors,
.f = ~ paste0(.x, " ~ ", paste0(.y, collapse = " + "))),
r_squared = purrr::map_dbl(.x = form,
.f = ~ calc_r_squared(form = .x,
data = data)),
vif = 1 / (1 - r_squared),
sqrt_vif = sqrt(vif),
tolerance = 1 / vif) %>%
dplyr::select(variable,
vif,
sqrt_vif,
tolerance,
r_squared) %>%
{.}
cor_mat <- cor(data,
method = method,
use = use)
#### Eigenvals, Conditional index --------------------------------
## deviation sscp (no intercept) ----------------
# Eigenvalues and condition index computed from correlation matrix without a
# constant.
if (method_for_eigen == "corr") {
svd_x <- svd(cor_mat)
res2 <- tibble::tibble(
variable = colnames(cor_mat),
eigenval = eigen(cor_mat)$values,
cond_index = sqrt(max(svd_x$d) / svd_x$d),
rnk = rank(dplyr::desc(eigenval))
) %>%
dplyr::select(variable, rnk, eigenval, cond_index)
res <- res %>%
dplyr::left_join(.,
res2,
by = "variable")
}
## scaled raw sscp (w/ intercept) ----------------
# By default the eigenvalues and condition index are computed on the scaled
# raw score SSCP matrix with an intercept.
if (method_for_eigen == "sscp") {
sscp <- data %>%
mutate(constant = 1) %>%
as.matrix() %>%
crossprod()
diag_1 <- sscp * diag(ncol(sscp))
diag_1 <- sqrt(diag_1)
diag_1 <- syminv(diag_1)
sscp <- diag_1 %*% sscp %*% diag_1
svd_x <- svd(sscp)
res2 <- tibble::tibble(
variable = c(colnames(data), "Intercept"),
eigenval = eigen(sscp)$values,
cond_index = sqrt(max(svd_x$d) / svd_x$d),
rnk = rank(dplyr::desc(eigenval))
) %>%
dplyr::select(variable, rnk, eigenval, cond_index)
res <- res %>%
dplyr::bind_rows(.,
tibble::tibble(variable = "Intercept",
vif = NA_real_,
sqrt_vif = NA_real_,
tolerance = NA_real_,
r_squared = NA_real_)) %>%
dplyr::left_join(.,
res2,
by = "variable")
}
#### Summary results --------------------------------
summary_res <- tibble::tibble(
info = c("Mean VIF",
"Condition Number",
"Determinant of Correlation Matrix"),
rstls = c(mean(res$vif, na.rm = TRUE),
max(res$cond_index),
det(cor_mat))
)
results <- list(table = res,
summary = summary_res)
#### Inverse correlation matrix --------------------------------
if (show_inv_cor_mat == TRUE) {
inv_cor_mat <- cor_mat %>%
solve(.) %>%
round(.,
digits = 5)
results <- list(table = res,
summary = summary_res,
inv_cor_mat = inv_cor_mat)
}
#### End of function --------------------------------
return(results)
}
#' Calculate R-Squared Value
#'
#' This helper function computes the R-squared value for a given formula and dataset.
#'
#' @param form A formula specifying the regression model (e.g., `"y ~ x1 + x2"`).
#' @param data A data frame containing the variables used in the formula.
#'
#' @importFrom stats lm
#'
#' @return The R-squared value from the linear model.
#'
#' @examples
#' data <- mtcars
#' form <- "mpg ~ disp + hp + wt"
#' calc_r_squared(form, data)
#'
#' @export
calc_r_squared <- function(form, data) {
# One way - old version
# mod1 <- glm(as.formula(form),
# data = data,
# family = gaussian(link = "identity"))
#
# # rsq::rsq(mod1)
# with(summary(mod1), 1 - deviance/null.deviance)
# Another way
# mod1 <- lm(as.formula(form),
# data = data)
#
# summary(mod1)$r.squared
# Manual method
# Fit the model
model <- lm(as.formula(form), data = data)
y <- purrr::pluck(model, "model", 1)
# Predicted values
y_pred <- predict(model)
# Residual sum of squares (SSR)
ssr <- sum((y - y_pred)^2)
# Total sum of squares (SST)
sst <- sum((y - mean(y))^2)
# R-squared
r_squared_manual <- 1 - (ssr / sst)
return(r_squared_manual)
}
#' Symmetric Inverse
#'
#' Computes the inverse of a symmetric positive-definite matrix using its Cholesky decomposition.
#'
#' @param x A symmetric positive-definite matrix.
#'
#' @return The inverse of the input matrix.
#'
#' @examples
#' mat <- matrix(c(4, 2, 2, 3), ncol = 2)
#' syminv(mat)
#'
#' @export
syminv <- function(x) {
# https://rdrr.io/cran/MNM/src/R/syminv.R
# http://www.philender.com/courses/multivariate/notes/magic.html
ch_x <- chol(x)
chol2inv(ch_x)
}
#' Convert a Column to Numeric Codes
#'
#' This function converts a character or factor column into numeric codes, preserving numeric columns as-is. Character and factor variables are first converted to factors and then assigned numeric codes based on their levels.
#'
#' @param col A vector (column) to be converted. It can be a character, factor, or numeric vector.
#'
#' @return A numeric vector. If the input is a character or factor column, it is converted to numeric codes. Numeric columns are returned unchanged.
#'
#' @examples
#' # Example usage
#' char_col <- c("a", "b", "a", "c")
#' factor_col <- factor(c("low", "medium", "high"))
#' numeric_col <- c(1.2, 3.4, 5.6)
#'
#' # Convert columns to numeric codes
#' make_numeric(char_col) # Returns numeric codes for characters
#' make_numeric(factor_col) # Returns numeric codes for factors
#' make_numeric(numeric_col) # Returns numeric values unchanged
#'
#' @export
make_numeric <- function(col) {
if (is.character(col) || is.factor(col)) {
as.numeric(as.factor(col)) # Convert characters or factors to numeric codes
} else {
col # Leave numeric columns as is
}
}
# lahigh <- tibble::tribble(
# ~id, ~gender, ~ethnic, ~school, ~algebra, ~math, ~eng95, ~eng94, ~mathnce, ~langnce, ~mathpr, ~langpr, ~biling, ~engprof, ~daysatt, ~daysabs,
# 1001L, "male", "hispanic", 1L, 3L, 0L, 2L, 2L, 56.98883, 42.45086, 63L, 36L, 2L, 2L, 73L, 4L,
# 1002L, "male", "hispanic", 1L, 1L, 2L, 2L, 4L, 37.09416, 46.82059, 27L, 44L, 2L, 3L, 73L, 4L,
# 1003L, "female", "hispanic", 1L, 3L, 3L, 4L, 3L, 32.27546, 43.56657, 20L, 38L, 2L, 3L, 76L, 2L,
# 1004L, "female", "hispanic", 1L, 1L, 4L, 3L, 4L, 29.05672, 43.56657, 16L, 38L, 2L, 2L, 74L, 3L,
# 1005L, "female", "hispanic", 1L, 0L, 1L, 0L, 2L, 6.748048, 27.24847, 2L, 14L, 3L, 1L, 73L, 3L,
# 1006L, "female", "hispanic", 1L, 4L, 1L, 3L, 4L, 61.65428, 48.41482, 71L, 47L, 0L, 1L, 62L, 13L,
# 1007L, "female", "hispanic", 1L, 0L, 1L, 1L, 3L, 56.98883, 40.73543, 63L, 33L, 2L, 2L, 66L, 11L,
# 1008L, "male", "hispanic", 1L, 0L, 0L, 0L, 0L, 10.39049, 15.35938, 3L, 5L, 2L, 1L, 72L, 7L,
# 1009L, "male", "hispanic", 1L, 2L, 2L, 3L, 2L, 50.52795, 52.11514, 51L, 54L, 2L, 1L, 63L, 10L,
# 1010L, "male", "filipino", 1L, 0L, 2L, 0L, 1L, 49.47205, 42.45086, 49L, 36L, 0L, 0L, 68L, 9L,
# 1011L, "female", "filipino", 1L, 1L, 0L, 1L, 1L, 39.55739, 36.45115, 31L, 26L, 0L, 0L, 72L, 4L,
# 1012L, "male", "hispanic", 1L, 4L, 4L, 3L, 4L, 33.73761, 13.13055, 22L, 4L, 2L, 2L, 74L, 5L,
# 1013L, "female", "hispanic", 1L, 3L, 4L, 3L, 3L, 62.90584, 62.27464, 73L, 72L, 2L, 2L, 72L, 5L,
# 1014L, "female", "afr-amer", 1L, 0L, 2L, 2L, 3L, 65.56011, 44.66451, 77L, 40L, 0L, 0L, 74L, 3L,
# 1015L, "male", "filipino", 1L, 0L, 3L, 1L, 1L, 23.01052, 25.25478, 10L, 12L, 1L, 0L, 76L, 1L,
# 1016L, "male", "hispanic", 1L, 4L, 3L, 4L, 2L, 75.83068, 61.04388, 89L, 70L, 2L, 2L, 76L, 0L,
# 1017L, "female", "hispanic", 1L, 2L, 2L, 4L, 4L, 41.31353, 49.47205, 34L, 49L, 2L, 1L, 75L, 1L,
# 1018L, "female", "hispanic", 1L, 0L, 2L, 4L, 3L, 41.88515, 65.56011, 35L, 77L, 2L, 1L, 74L, 0L,
# 1019L, "male", "afr-amer", 1L, 1L, 2L, 2L, 1L, 65.56011, 46.82059, 77L, 44L, 1L, 0L, 75L, 2L,
# 1020L, "male", "hispanic", 1L, 3L, 0L, 0L, 0L, 13.13055, 6.748048, 4L, 2L, 3L, 2L, 55L, 24L,
# 1021L, "female", "hispanic", 1L, 0L, 1L, 3L, 2L, 33.01677, 42.45086, 21L, 36L, 2L, 3L, 75L, 2L,
# 1022L, "male", "hispanic", 1L, 0L, 2L, 2L, 2L, 55.88246, 64.87473, 61L, 76L, 2L, 1L, 76L, 0L,
# 1023L, "male", "hispanic", 1L, 3L, 4L, 3L, 3L, 45.2079, 55.33549, 41L, 60L, 2L, 1L, 76L, 1L,
# 1024L, "male", "hispanic", 1L, 2L, 2L, 2L, 2L, 56.98883, 44.66451, 63L, 40L, 2L, 2L, 76L, 0L,
# 1025L, "female", "hispanic", 1L, 3L, 4L, 4L, 3L, 31.5115, 38.34572, 19L, 29L, 2L, 1L, 71L, 8L,
# 1026L, "male", "afr-amer", 1L, 0L, 2L, 3L, 3L, 52.64643, 50, 55L, 50L, 0L, 0L, 67L, 3L,
# 1027L, "male", "hispanic", 1L, 0L, 1L, 0L, 2L, 17.25647, 6.748048, 6L, 2L, 0L, 0L, 70L, 7L,
# 1028L, "female", "hispanic", 1L, 0L, 2L, 1L, 2L, 33.01677, 40.15026, 21L, 32L, 2L, 2L, 76L, 0L,
# 1029L, "male", "hispanic", 1L, 3L, 1L, 2L, 2L, 61.04388, 57.54914, 70L, 64L, 1L, 1L, 74L, 2L,
# 1030L, "male", "afr-amer", 1L, 1L, 4L, 2L, 3L, 66.98323, 71.82729, 79L, 85L, 0L, 0L, 77L, 0L,
# 1031L, "male", "hispanic", 1L, 1L, 1L, 1L, 1L, 1.007114, 45.2079, 1L, 41L, 1L, 4L, 77L, 0L,
# 1032L, "female", "hispanic", 1L, 1L, 4L, 2L, 3L, 38.34572, 35.12527, 29L, 24L, 3L, 1L, 76L, 1L,
# 1033L, "male", "hispanic", 1L, 1L, 3L, 3L, 1L, 44.66451, 46.82059, 40L, 44L, 2L, 2L, 32L, 3L,
# 1034L, "male", "asian", 1L, 2L, 4L, 3L, 2L, 44.11754, 46.82059, 39L, 44L, 3L, 2L, 77L, 0L,
# 1035L, "male", "hispanic", 1L, 2L, 3L, 2L, 0L, 59.84974, 46.28556, 68L, 43L, 3L, 2L, 77L, 0L,
# 1036L, "female", "hispanic", 1L, 0L, 4L, 0L, 3L, 32.27546, 47.35357, 20L, 45L, 3L, 1L, 49L, 28L,
# 1037L, "male", "hispanic", 1L, 0L, 0L, 2L, 1L, 23.01052, 49.47205, 10L, 49L, 1L, 0L, 71L, 8L,
# 1038L, "male", "hispanic", 1L, 2L, 2L, 3L, 3L, 70.94328, 61.04388, 84L, 70L, 2L, 4L, 72L, 5L,
# 1039L, "male", "afr-amer", 1L, 0L, 2L, 1L, 0L, 1.007114, 1.007114, 1L, 1L, 0L, 0L, 75L, 2L,
# 1040L, "female", "hispanic", 1L, 0L, 0L, 1L, 0L, 41.88515, 52.11514, 35L, 54L, 3L, 2L, 46L, 27L,
# 1041L, "female", "hispanic", 1L, 3L, 3L, 3L, 4L, 40.15026, 35.12527, 32L, 24L, 2L, 2L, 72L, 5L,
# 1042L, "female", "hispanic", 1L, 0L, 1L, 0L, 2L, 41.31353, 38.34572, 34L, 29L, 3L, 2L, 59L, 18L,
# 1043L, "female", "hispanic", 1L, 0L, 4L, 2L, 3L, 44.66451, 58.68647, 40L, 66L, 3L, 0L, 57L, 19L,
# 1044L, "male", "hispanic", 1L, 1L, 2L, 1L, 1L, 38.34572, 42.45086, 29L, 36L, 2L, 2L, 67L, 9L,
# 1045L, "male", "hispanic", 1L, 2L, 3L, 0L, 0L, 32.27546, 1.007114, 20L, 1L, 1L, 2L, 68L, 9L,
# 1046L, "female", "hispanic", 1L, 3L, 4L, 3L, 1L, 37.09416, 32.27546, 27L, 20L, 0L, 1L, 75L, 4L,
# 1047L, "male", "hispanic", 1L, 2L, 2L, 2L, 0L, 63.54885, 57.54914, 74L, 64L, 2L, 1L, 75L, 2L,
# 1048L, "male", "hispanic", 1L, 1L, 2L, 2L, 2L, 43.56657, 41.31353, 38L, 34L, 1L, 1L, 68L, 3L,
# 1049L, "male", "hispanic", 1L, 0L, 0L, 2L, 0L, 33.01677, 24.16932, 21L, 11L, 0L, 1L, 68L, 9L,
# 1050L, "female", "asian", 1L, 0L, 0L, 0L, 3L, 68.48849, 59.26457, 81L, 67L, 2L, 1L, 56L, 20L,
# 1051L, "male", "hispanic", 1L, 0L, 3L, 0L, 2L, 29.05672, 21.7637, 16L, 9L, 1L, 0L, 65L, 6L,
# 1052L, "male", "asian", 1L, 4L, 2L, 4L, 2L, 54.7921, 54.7921, 59L, 59L, 0L, 1L, 76L, 0L,
# 1053L, "male", "hispanic", 1L, 0L, 0L, 0L, 2L, 48.94376, 51.58518, 48L, 53L, 2L, 1L, 50L, 27L,
# 1054L, "female", "hispanic", 1L, 2L, 4L, 2L, 3L, 52.64643, 50.52795, 55L, 51L, 2L, 1L, 65L, 12L,
# 1055L, "female", "hispanic", 1L, 0L, 0L, 0L, 0L, 13.13055, 32.27546, 4L, 20L, 3L, 1L, 43L, 34L,
# 1056L, "male", "asian", 1L, 3L, 0L, 2L, 0L, 53.71444, 41.88515, 57L, 35L, 1L, 4L, 76L, 1L,
# 1057L, "male", "afr-amer", 1L, 1L, 0L, 1L, 1L, 15.35938, 32.27546, 5L, 20L, 0L, 0L, 52L, 25L,
# 1058L, "male", "afr-amer", 1L, 0L, 2L, 0L, 0L, 10.39049, 17.25647, 3L, 6L, 0L, 0L, 71L, 5L,
# 1059L, "female", "hispanic", 1L, 1L, 2L, 2L, 3L, 34.43988, 38.34572, 23L, 29L, 3L, 3L, 74L, 3L,
# 1060L, "female", "hispanic", 1L, 3L, 2L, 4L, 2L, 41.88515, 42.45086, 35L, 36L, 1L, 1L, 77L, 2L,
# 1061L, "male", "hispanic", 1L, 0L, 0L, 1L, 1L, 40.73543, 55.33549, 33L, 60L, 3L, 2L, 76L, 1L,
# 1062L, "female", "hispanic", 1L, 1L, 1L, 2L, 1L, 37.09416, 52.64643, 27L, 55L, 2L, 2L, 70L, 7L,
# 1063L, "male", "hispanic", 1L, 1L, 2L, 3L, 3L, 26.2782, 26.2782, 13L, 13L, 1L, 1L, 73L, 4L,
# 1064L, "male", "hispanic", 1L, 2L, 0L, 3L, 1L, 47.88486, 36.45115, 46L, 26L, 3L, 1L, 71L, 8L,
# 1065L, "female", "hispanic", 1L, 0L, 0L, 1L, 0L, 38.95612, 55.88246, 30L, 61L, 0L, 0L, 71L, 6L,
# 1066L, "male", "asian", 1L, 0L, 0L, 0L, 1L, 40.15026, 47.35357, 32L, 45L, 0L, 0L, 61L, 16L,
# 1067L, "female", "afr-amer", 1L, 0L, 1L, 3L, 2L, 36.45115, 40.15026, 26L, 32L, 0L, 0L, 74L, 3L,
# 1068L, "female", "hispanic", 1L, 0L, 2L, 1L, 2L, 27.24847, 39.55739, 14L, 31L, 1L, 2L, 71L, 4L,
# 1069L, "female", "filipino", 1L, 1L, 3L, 3L, 3L, 39.55739, 43.56657, 31L, 38L, 1L, 0L, 73L, 3L,
# 1070L, "female", "hispanic", 1L, 0L, 2L, 1L, 1L, 48.94376, 36.45115, 48L, 26L, 3L, 3L, 72L, 5L,
# 1071L, "male", "hispanic", 1L, 2L, 3L, 3L, 2L, 62.27464, 46.28556, 72L, 43L, 1L, 0L, 73L, 0L,
# 1072L, "male", "hispanic", 1L, 2L, 3L, 2L, 3L, 66.98323, 59.84974, 79L, 68L, 0L, 1L, 67L, 9L,
# 1073L, "male", "filipino", 1L, 2L, 2L, 3L, 3L, 28.17271, 59.84974, 15L, 68L, 3L, 0L, 77L, 0L,
# 1074L, "male", "hispanic", 1L, 0L, 0L, 0L, 0L, 35.12527, 37.09416, 24L, 27L, 1L, 1L, 69L, 8L,
# 1075L, "female", "filipino", 1L, 3L, 4L, 4L, 3L, 52.64643, 70.09472, 55L, 83L, 0L, 0L, 77L, 0L,
# 1076L, "female", "afr-amer", 1L, 0L, 3L, 3L, 3L, 26.2782, 35.12527, 13L, 24L, 0L, 0L, 65L, 11L,
# 1077L, "male", "hispanic", 1L, 3L, 4L, 1L, 3L, 41.31353, 42.45086, 34L, 36L, 0L, 1L, 75L, 4L,
# 1078L, "male", "hispanic", 1L, 2L, 1L, 2L, 2L, 59.26457, 71.82729, 67L, 85L, 1L, 1L, 75L, 2L,
# 1079L, "male", "hispanic", 1L, 0L, 0L, 0L, 0L, 1.007114, 17.25647, 1L, 6L, 3L, 1L, 35L, 35L,
# 1080L, "female", "hispanic", 1L, 0L, 0L, 0L, 2L, 33.01677, 41.88515, 21L, 35L, 3L, 0L, 54L, 23L,
# 1081L, "female", "hispanic", 1L, 0L, 4L, 0L, 3L, 40.73543, 42.45086, 33L, 36L, 3L, 2L, 64L, 13L,
# 1082L, "male", "hispanic", 1L, 2L, 4L, 2L, 4L, 66.26239, 64.87473, 78L, 76L, 0L, 1L, 71L, 6L,
# 1083L, "female", "afr-amer", 1L, 4L, 2L, 3L, 2L, 70.94328, 45.74812, 84L, 42L, 0L, 0L, 79L, 0L,
# 1084L, "male", "hispanic", 1L, 2L, 0L, 3L, 1L, 54.7921, 60.44261, 59L, 69L, 2L, 2L, 71L, 6L,
# 1085L, "male", "hispanic", 1L, 3L, 1L, 2L, 2L, 64.20476, 50.52795, 75L, 51L, 2L, 1L, 77L, 0L,
# 1086L, "male", "afr-amer", 1L, 1L, 2L, 2L, 1L, 33.73761, 40.15026, 22L, 32L, 0L, 0L, 66L, 8L,
# 1087L, "female", "hispanic", 1L, 0L, 3L, 1L, 2L, 49.47205, 44.66451, 49L, 40L, 0L, 0L, 66L, 11L,
# 1088L, "female", "hispanic", 1L, 0L, 3L, 4L, 2L, 26.2782, 73.72179, 13L, 87L, 2L, 1L, 66L, 11L,
# 1089L, "male", "filipino", 1L, 4L, 3L, 4L, 3L, 70.94328, 54.25188, 84L, 58L, 1L, 3L, 73L, 4L,
# 1090L, "male", "hispanic", 1L, 0L, 0L, 0L, 1L, 37.09416, 41.31353, 27L, 34L, 2L, 2L, 71L, 6L,
# 1091L, "female", "hispanic", 1L, 1L, 4L, 2L, 4L, 37.09416, 49.47205, 27L, 49L, 0L, 3L, 54L, 23L,
# 1092L, "female", "hispanic", 1L, 3L, 2L, 2L, 2L, 61.04388, 69.27759, 70L, 82L, 1L, 1L, 72L, 5L,
# 1093L, "male", "hispanic", 1L, 1L, 3L, 4L, 2L, 86.86945, 86.86945, 96L, 96L, 2L, 2L, 72L, 5L,
# 1094L, "female", "afr-amer", 1L, 0L, 0L, 0L, 0L, 61.04388, 64.20476, 70L, 75L, 0L, 0L, 51L, 26L,
# 1095L, "female", "hispanic", 1L, 0L, 2L, 3L, 4L, 23.01052, 6.748048, 10L, 2L, 3L, 3L, 69L, 7L,
# 1096L, "male", "hispanic", 1L, 0L, 1L, 0L, 2L, 27.24847, 35.12527, 14L, 24L, 3L, 1L, 76L, 1L,
# 1097L, "male", "hispanic", 1L, 0L, 1L, 3L, 2L, 32.27546, 46.82059, 20L, 44L, 2L, 2L, 68L, 9L,
# 1098L, "male", "hispanic", 1L, 0L, 0L, 0L, 0L, 24.16932, 17.25647, 11L, 6L, 2L, 2L, 66L, 11L,
# 1099L, "male", "hispanic", 1L, 0L, 2L, 0L, 0L, 45.74812, 50, 42L, 50L, 2L, 1L, 60L, 18L,
# 1100L, "male", "hispanic", 1L, 0L, 1L, 0L, 0L, 6.748048, 13.13055, 2L, 4L, 3L, 2L, 56L, 12L,
# 1101L, "male", "afr-amer", 1L, 0L, 0L, 0L, 0L, 35.12527, 27.24847, 24L, 14L, 0L, 0L, 73L, 3L,
# 1102L, "male", "asian", 1L, 0L, 3L, 1L, 3L, 43.01117, 28.17271, 37L, 15L, 3L, 0L, 69L, 0L,
# 1103L, "male", "hispanic", 1L, 0L, 0L, 2L, 0L, 26.2782, 13.13055, 13L, 4L, 3L, 1L, 73L, 4L,
# 1104L, "male", "hispanic", 1L, 2L, 1L, 1L, 1L, 10.39049, 29.05672, 3L, 16L, 3L, 0L, 68L, 10L,
# 1105L, "male", "afr-amer", 1L, 1L, 3L, 2L, 4L, 61.04388, 66.26239, 70L, 78L, 0L, 0L, 61L, 16L,
# 1106L, "female", "hispanic", 1L, 1L, 1L, 2L, 3L, 37.09416, 51.58518, 27L, 53L, 2L, 2L, 74L, 1L,
# 1107L, "female", "afr-amer", 1L, 0L, 2L, 4L, 1L, 1.007114, 1.007114, 1L, 1L, 0L, 0L, 70L, 9L,
# 1108L, "female", "asian", 1L, 1L, 4L, 3L, 3L, 55.88246, 45.2079, 61L, 41L, 2L, 0L, 74L, 3L,
# 1109L, "male", "hispanic", 1L, 3L, 3L, 3L, 3L, 46.82059, 38.34572, 44L, 29L, 3L, 3L, 77L, 0L,
# 1110L, "male", "hispanic", 1L, 0L, 0L, 0L, 0L, 41.88515, 56.98883, 35L, 63L, 2L, 3L, 68L, 9L,
# 1111L, "male", "asian", 1L, 3L, 0L, 2L, 2L, 66.26239, 35.79525, 78L, 25L, 3L, 0L, 65L, 14L,
# 1112L, "female", "hispanic", 1L, 0L, 3L, 2L, 2L, 10.39049, 38.95612, 3L, 30L, 2L, 2L, 70L, 7L,
# 1113L, "male", "hispanic", 1L, 0L, 1L, 0L, 1L, 33.01677, 40.15026, 21L, 32L, 3L, 4L, 74L, 3L,
# 1114L, "male", "hispanic", 1L, 0L, 0L, 3L, 4L, 36.45115, 20.40919, 26L, 8L, 3L, 3L, 67L, 10L,
# 1115L, "male", "hispanic", 1L, 0L, 3L, 2L, 2L, 46.82059, 65.56011, 44L, 77L, 2L, 1L, 64L, 12L,
# 1116L, "female", "hispanic", 1L, 2L, 1L, 2L, 0L, 48.41482, 34.43988, 47L, 23L, 1L, 0L, 71L, 6L,
# 1117L, "female", "hispanic", 1L, 0L, 0L, 1L, 2L, 41.88515, 41.88515, 35L, 35L, 2L, 0L, 42L, 35L,
# 1118L, "female", "afr-amer", 1L, 3L, 3L, 4L, 3L, 20.40919, 25.25478, 8L, 12L, 0L, 0L, 64L, 13L,
# 1119L, "female", "hispanic", 1L, 3L, 1L, 4L, 3L, 73.72179, 74.74522, 87L, 88L, 2L, 1L, 74L, 3L,
# 1120L, "male", "hispanic", 1L, 0L, 2L, 3L, 2L, 10.39049, 40.15026, 3L, 32L, 3L, 2L, 65L, 10L,
# 1121L, "male", "hispanic", 1L, 0L, 0L, 1L, 2L, 17.25647, 20.40919, 6L, 8L, 3L, 3L, 71L, 6L,
# 1122L, "male", "afr-amer", 1L, 4L, 3L, 4L, 3L, 75.83068, 64.87473, 89L, 76L, 0L, 0L, 76L, 0L,
# 1123L, "male", "hispanic", 1L, 1L, 1L, 1L, 0L, 26.2782, 23.01052, 13L, 10L, 3L, 1L, 75L, 2L,
# 1124L, "male", "hispanic", 1L, 0L, 3L, 3L, 4L, 70.94328, 82.74353, 84L, 94L, 2L, 1L, 71L, 6L,
# 1125L, "male", "hispanic", 1L, 4L, 4L, 2L, 2L, 76.98948, 68.48849, 90L, 81L, 1L, 0L, 72L, 5L,
# 1126L, "female", "hispanic", 1L, 1L, 4L, 3L, 4L, 61.65428, 58.11485, 71L, 65L, 2L, 2L, 62L, 13L,
# 1127L, "female", "afr-amer", 1L, 0L, 0L, 2L, 1L, 28.17271, 6.748048, 15L, 2L, 0L, 0L, 73L, 4L,
# 1128L, "female", "hispanic", 1L, 0L, 2L, 0L, 2L, 45.2079, 48.94376, 41L, 48L, 2L, 1L, 72L, 5L,
# 1129L, "female", "asian", 1L, 4L, 3L, 4L, 3L, 56.98883, 65.56011, 63L, 77L, 0L, 0L, 74L, 3L,
# 1130L, "female", "hispanic", 1L, 0L, 1L, 0L, 1L, 41.31353, 48.94376, 34L, 48L, 2L, 2L, 44L, 30L,
# 1131L, "female", "hispanic", 1L, 0L, 1L, 1L, 1L, 47.35357, 46.82059, 45L, 44L, 0L, 2L, 61L, 16L,
# 1132L, "female", "hispanic", 1L, 1L, 0L, 0L, 1L, 38.34572, 43.01117, 29L, 37L, 0L, 2L, 62L, 15L,
# 1133L, "female", "hispanic", 1L, 1L, 2L, 1L, 0L, 10.39049, 6.748048, 3L, 2L, 3L, 2L, 65L, 12L,
# 1134L, "male", "hispanic", 1L, 3L, 0L, 4L, 1L, 41.88515, 36.45115, 35L, 26L, 2L, 4L, 78L, 1L,
# 1135L, "male", "afr-amer", 1L, 1L, 2L, 3L, 2L, 40.15026, 38.95612, 32L, 30L, 0L, 0L, 72L, 1L,
# 1136L, "male", "hispanic", 1L, 0L, 3L, 2L, 2L, 33.73761, 35.79525, 22L, 25L, 0L, 0L, 70L, 7L,
# 1137L, "female", "hispanic", 1L, 4L, 1L, 4L, 4L, 68.48849, 52.64643, 81L, 55L, 1L, 2L, 74L, 1L,
# 1138L, "female", "asian", 1L, 0L, 2L, 0L, 3L, 98.99289, 64.20476, 99L, 75L, 2L, 2L, 13L, 45L,
# 1139L, "female", "hispanic", 1L, 4L, 2L, 3L, 4L, 62.90584, 43.01117, 73L, 37L, 2L, 3L, 69L, 10L,
# 1140L, "male", "asian", 1L, 3L, 3L, 3L, 3L, 60.44261, 36.45115, 69L, 26L, 2L, 4L, 74L, 3L,
# 1141L, "female", "afr-amer", 1L, 1L, 0L, 2L, 1L, 37.09416, 10.39049, 27L, 3L, 0L, 0L, 52L, 27L,
# 1142L, "female", "hispanic", 1L, 2L, 1L, 2L, 2L, 26.2782, 33.01677, 13L, 21L, 2L, 2L, 74L, 2L,
# 1143L, "female", "hispanic", 1L, 0L, 0L, 1L, 1L, 64.87473, 53.71444, 76L, 57L, 2L, 1L, 58L, 13L,
# 1144L, "female", "afr-amer", 1L, 0L, 2L, 3L, 2L, 18.91984, 29.05672, 7L, 16L, 0L, 0L, 70L, 2L,
# 1145L, "male", "hispanic", 1L, 0L, 2L, 0L, 2L, 54.7921, 47.88486, 59L, 46L, 2L, 1L, 74L, 5L,
# 1146L, "female", "hispanic", 1L, 0L, 2L, 2L, 4L, 38.34572, 38.95612, 29L, 30L, 2L, 1L, 64L, 5L,
# 1147L, "female", "hispanic", 1L, 0L, 4L, 1L, 4L, 53.71444, 52.11514, 57L, 54L, 2L, 2L, 69L, 4L,
# 1148L, "female", "hispanic", 1L, 3L, 0L, 4L, 3L, 46.82059, 51.58518, 44L, 53L, 1L, 3L, 76L, 3L,
# 1149L, "female", "hispanic", 1L, 0L, 3L, 3L, 3L, 51.58518, 71.82729, 53L, 85L, 1L, 1L, 44L, 20L,
# 1150L, "female", "hispanic", 1L, 0L, 1L, 1L, 2L, 34.43988, 40.15026, 23L, 32L, 3L, 1L, 63L, 12L,
# 1151L, "female", "afr-amer", 1L, 2L, 0L, 4L, 0L, 38.34572, 44.66451, 29L, 40L, 0L, 0L, 48L, 31L,
# 1152L, "male", "asian", 1L, 0L, 2L, 2L, 2L, 44.66451, 40.73543, 40L, 33L, 3L, 0L, 70L, 6L,
# 1153L, "male", "hispanic", 1L, 0L, 4L, 2L, 0L, 49.47205, 31.5115, 49L, 19L, 2L, 3L, 63L, 14L,
# 1154L, "female", "afr-amer", 1L, 0L, 3L, 0L, 3L, 43.56657, 46.82059, 38L, 44L, 0L, 0L, 56L, 13L,
# 1155L, "male", "afr-amer", 1L, 0L, 2L, 3L, 4L, 39.55739, 49.47205, 31L, 49L, 0L, 0L, 71L, 6L,
# 1156L, "female", "afr-amer", 1L, 0L, 0L, 0L, 0L, 33.01677, 47.35357, 21L, 45L, 0L, 0L, 65L, 12L,
# 1157L, "male", "afr-amer", 1L, 0L, 2L, 0L, 0L, 20.40919, 29.05672, 8L, 16L, 0L, 0L, 65L, 12L,
# 1158L, "male", "hispanic", 1L, 3L, 0L, 2L, 3L, 43.01117, 34.43988, 37L, 23L, 3L, 3L, 77L, 0L,
# 1159L, "male", "hispanic", 1L, 3L, 4L, 4L, 3L, 51.58518, 43.56657, 53L, 38L, 2L, 1L, 78L, 1L,
# 2001L, "female", "white", 2L, 0L, 1L, 0L, 3L, 39.55739, 50.52795, 31L, 51L, 0L, 0L, 82L, 4L,
# 2002L, "male", "white", 2L, 2L, 1L, 2L, 1L, 53.71444, 1.007114, 57L, 1L, 3L, 0L, 86L, 0L,
# 2003L, "male", "filipino", 2L, 1L, 2L, 2L, 1L, 53.71444, 38.95612, 57L, 30L, 0L, 0L, 86L, 0L,
# 2004L, "male", "white", 2L, 1L, 2L, 2L, 3L, 54.7921, 64.20476, 59L, 75L, 1L, 0L, 84L, 2L,
# 2005L, "female", "white", 2L, 1L, 2L, 1L, 2L, 38.34572, 54.7921, 29L, 59L, 0L, 0L, 85L, 1L,
# 2006L, "female", "asian", 2L, 2L, 3L, 4L, 3L, 45.2079, 71.82729, 41L, 85L, 1L, 0L, 84L, 2L,
# 2007L, "male", "white", 2L, 2L, 3L, 3L, 2L, 61.65428, 58.68647, 71L, 66L, 0L, 0L, 86L, 0L,
# 2008L, "female", "white", 2L, 1L, 2L, 2L, 2L, 54.7921, 50, 59L, 50L, 3L, 0L, 86L, 0L,
# 2009L, "male", "white", 2L, 1L, 3L, 2L, 4L, 61.65428, 54.7921, 71L, 59L, 0L, 0L, 86L, 0L,
# 2010L, "female", "white", 2L, 1L, 4L, 3L, 2L, 61.04388, 58.68647, 70L, 66L, 0L, 0L, 79L, 7L,
# 2011L, "male", "white", 2L, 3L, 3L, 3L, 1L, 65.56011, 66.26239, 77L, 78L, 1L, 0L, 84L, 2L,
# 2012L, "female", "asian", 2L, 1L, 1L, 2L, 3L, 61.04388, 71.82729, 70L, 85L, 1L, 0L, 76L, 9L,
# 2013L, "female", "white", 2L, 1L, 4L, 3L, 3L, 73.72179, 55.33549, 87L, 60L, 2L, 0L, 80L, 6L,
# 2014L, "male", "white", 2L, 0L, 3L, 4L, 0L, 54.7921, 51.58518, 59L, 53L, 0L, 0L, 82L, 4L,
# 2015L, "male", "white", 2L, 1L, 3L, 2L, 2L, 58.11485, 58.11485, 65L, 65L, 0L, 0L, 85L, 1L,
# 2016L, "female", "hispanic", 2L, 1L, 3L, 2L, 3L, 37.72536, 46.82059, 28L, 44L, 2L, 3L, 79L, 7L,
# 2017L, "male", "white", 2L, 3L, 3L, 3L, 3L, 65.56011, 70.09472, 77L, 83L, 1L, 0L, 86L, 0L,
# 2018L, "male", "white", 2L, 3L, 2L, 3L, 3L, 58.11485, 68.48849, 65L, 81L, 1L, 0L, 86L, 0L,
# 2019L, "female", "white", 2L, 2L, 2L, 4L, 4L, 62.90584, 71.82729, 73L, 85L, 0L, 0L, 82L, 4L,
# 2020L, "male", "hispanic", 2L, 3L, 2L, 3L, 2L, 98.99289, 55.33549, 99L, 60L, 0L, 0L, 82L, 2L,
# 2021L, "female", "white", 2L, 3L, 3L, 4L, 3L, 53.71444, 66.98323, 57L, 79L, 2L, 2L, 86L, 0L,
# 2022L, "female", "white", 2L, 3L, 1L, 3L, 2L, 65.56011, 50, 77L, 50L, 0L, 0L, 82L, 4L,
# 2023L, "female", "hispanic", 2L, 3L, 2L, 4L, 2L, 53.71444, 65.56011, 57L, 77L, 0L, 0L, 84L, 2L,
# 2024L, "female", "afr-amer", 2L, 0L, 0L, 0L, 2L, 48.41482, 29.05672, 47L, 16L, 0L, 0L, 67L, 18L,
# 2025L, "female", "white", 2L, 0L, 3L, 3L, 3L, 35.12527, 52.11514, 24L, 54L, 2L, 0L, 85L, 1L,
# 2026L, "male", "white", 2L, 2L, 2L, 3L, 3L, 70.94328, 70.94328, 84L, 84L, 0L, 0L, 86L, 0L,
# 2027L, "female", "white", 2L, 2L, 3L, 3L, 3L, 62.90584, 65.56011, 73L, 77L, 2L, 0L, 85L, 1L,
# 2028L, "male", "white", 2L, 1L, 1L, 2L, 1L, 68.48849, 58.68647, 81L, 66L, 0L, 0L, 70L, 16L,
# 2029L, "female", "afr-amer", 2L, 1L, 0L, 0L, 2L, 51.05624, 41.31353, 52L, 34L, 0L, 0L, 79L, 6L,
# 2030L, "female", "white", 2L, 1L, 2L, 3L, 3L, 64.20476, 67.72454, 75L, 80L, 0L, 0L, 70L, 16L,
# 2031L, "male", "asian", 2L, 2L, 3L, 4L, 3L, 58.11485, 78.2363, 65L, 91L, 1L, 0L, 86L, 0L,
# 2032L, "female", "afr-amer", 2L, 0L, 2L, 2L, 3L, 46.82059, 42.45086, 44L, 36L, 0L, 0L, 77L, 8L,
# 2033L, "male", "white", 2L, 0L, 1L, 3L, 2L, 46.82059, 52.64643, 44L, 55L, 0L, 0L, 85L, 1L,
# 2034L, "female", "white", 2L, 3L, 3L, 4L, 4L, 66.98323, 86.86945, 79L, 96L, 0L, 0L, 84L, 2L,
# 2035L, "female", "white", 2L, 0L, 0L, 3L, 2L, 32.27546, 51.05624, 20L, 52L, 1L, 0L, 83L, 3L,
# 2036L, "female", "hispanic", 2L, 1L, 2L, 2L, 3L, 29.05672, 29.05672, 16L, 16L, 3L, 3L, 82L, 4L,
# 2037L, "female", "hispanic", 2L, 1L, 3L, 2L, 2L, 98.99289, 42.45086, 99L, 36L, 3L, 2L, 84L, 2L,
# 2038L, "female", "afr-amer", 2L, 3L, 2L, 4L, 2L, 61.65428, 84.64062, 71L, 95L, 0L, 0L, 82L, 4L,
# 2039L, "male", "white", 2L, 2L, 4L, 2L, 2L, 47.88486, 37.09416, 46L, 27L, 2L, 2L, 79L, 7L,
# 2040L, "female", "hispanic", 2L, 2L, 3L, 2L, 2L, 53.71444, 56.98883, 57L, 63L, 1L, 0L, 86L, 0L,
# 2041L, "female", "hispanic", 2L, 2L, 4L, 2L, 3L, 59.26457, 51.58518, 67L, 53L, 2L, 3L, 85L, 1L,
# 2042L, "female", "white", 2L, 4L, 2L, 4L, 4L, 73.72179, 93.25195, 87L, 98L, 0L, 0L, 85L, 1L,
# 2043L, "female", "white", 2L, 2L, 2L, 2L, 3L, 61.04388, 51.58518, 70L, 53L, 0L, 0L, 86L, 0L,
# 2044L, "female", "white", 2L, 0L, 1L, 1L, 1L, 33.01677, 45.2079, 21L, 41L, 0L, 0L, 73L, 13L,
# 2045L, "female", "white", 2L, 0L, 3L, 1L, 2L, 39.55739, 41.31353, 31L, 34L, 0L, 0L, 85L, 1L,
# 2046L, "male", "white", 2L, 3L, 2L, 4L, 2L, 56.98883, 62.27464, 63L, 72L, 2L, 0L, 86L, 0L,
# 2047L, "female", "hispanic", 2L, 2L, 4L, 3L, 3L, 46.82059, 47.88486, 44L, 46L, 2L, 2L, 85L, 1L,
# 2048L, "male", "white", 2L, 2L, 2L, 3L, 2L, 41.31353, 44.66451, 34L, 40L, 3L, 0L, 86L, 0L,
# 2049L, "female", "afr-amer", 2L, 2L, 3L, 3L, 4L, 65.56011, 71.82729, 77L, 85L, 0L, 0L, 85L, 1L,
# 2050L, "female", "white", 2L, 1L, 2L, 3L, 3L, 82.74353, 98.99289, 94L, 99L, 1L, 0L, 86L, 0L,
# 2051L, "female", "afr-amer", 2L, 0L, 2L, 3L, 3L, 45.2079, 44.11754, 41L, 39L, 0L, 0L, 85L, 1L,
# 2052L, "female", "white", 2L, 2L, 3L, 3L, 4L, 59.26457, 61.04388, 67L, 70L, 1L, 0L, 86L, 0L,
# 2053L, "female", "white", 2L, 1L, 2L, 2L, 2L, 55.88246, 56.98883, 61L, 63L, 1L, 0L, 84L, 2L,
# 2054L, "male", "white", 2L, 4L, 3L, 4L, 2L, 69.27759, 79.59081, 82L, 92L, 0L, 0L, 86L, 0L,
# 2055L, "female", "afr-amer", 2L, 3L, 3L, 3L, 2L, 56.98883, 59.26457, 63L, 67L, 0L, 0L, 85L, 1L,
# 2056L, "male", "white", 2L, 3L, 4L, 3L, 2L, 56.98883, 47.35357, 63L, 45L, 3L, 1L, 86L, 0L,
# 2057L, "female", "white", 2L, 3L, 4L, 4L, 3L, 65.56011, 62.27464, 77L, 72L, 1L, 0L, 82L, 4L,
# 2058L, "male", "white", 2L, 1L, 2L, 3L, 2L, 47.88486, 51.05624, 46L, 52L, 0L, 0L, 83L, 3L,
# 2059L, "male", "white", 2L, 1L, 2L, 2L, 2L, 20.40919, 40.15026, 8L, 32L, 1L, 0L, 85L, 1L,
# 2060L, "female", "hispanic", 2L, 3L, 4L, 3L, 4L, 55.88246, 81.08016, 61L, 93L, 1L, 0L, 86L, 0L,
# 2061L, "female", "asian", 2L, 3L, 1L, 2L, 3L, 61.65428, 60.44261, 71L, 69L, 0L, 0L, 85L, 1L,
# 2062L, "female", "white", 2L, 3L, 4L, 4L, 4L, 58.11485, 68.48849, 65L, 81L, 0L, 0L, 82L, 4L,
# 2063L, "female", "hispanic", 2L, 1L, 4L, 2L, 3L, 45.2079, 47.35357, 41L, 45L, 1L, 0L, 85L, 1L,
# 2064L, "male", "hispanic", 2L, 0L, 0L, 0L, 0L, 29.05672, 32.27546, 16L, 20L, 2L, 2L, 77L, 9L,
# 2065L, "female", "white", 2L, 2L, 2L, 3L, 3L, 33.73761, 59.84974, 22L, 68L, 0L, 0L, 86L, 0L,
# 2066L, "male", "hispanic", 2L, 1L, 1L, 1L, 2L, 53.71444, 40.15026, 57L, 32L, 2L, 2L, 82L, 4L,
# 2067L, "female", "asian", 2L, 3L, 2L, 3L, 1L, 50.52795, 53.71444, 51L, 57L, 2L, 0L, 54L, 8L,
# 2068L, "male", "hispanic", 2L, 0L, 2L, 1L, 0L, 63.54885, 54.25188, 74L, 58L, 0L, 1L, 73L, 13L,
# 2069L, "male", "white", 2L, 1L, 4L, 2L, 3L, 45.2079, 48.94376, 41L, 48L, 2L, 0L, 86L, 0L,
# 2070L, "male", "white", 2L, 2L, 2L, 1L, 4L, 73.72179, 56.43343, 87L, 62L, 2L, 0L, 86L, 0L,
# 2071L, "male", "white", 2L, 3L, 4L, 4L, 4L, 59.26457, 49.47205, 67L, 49L, 0L, 0L, 86L, 0L,
# 2072L, "female", "asian", 2L, 4L, 4L, 3L, 2L, 98.99289, 69.27759, 99L, 82L, 2L, 0L, 86L, 0L,
# 2073L, "female", "hispanic", 2L, 0L, 3L, 3L, 4L, 56.98883, 74.74522, 63L, 88L, 1L, 0L, 84L, 2L,
# 2074L, "female", "white", 2L, 2L, 4L, 3L, 3L, 58.11485, 58.11485, 65L, 65L, 0L, 0L, 81L, 5L,
# 2075L, "female", "white", 2L, 4L, 1L, 4L, 2L, 61.65428, 86.86945, 71L, 96L, 0L, 0L, 85L, 1L,
# 2076L, "male", "white", 2L, 2L, 2L, 4L, 2L, 65.56011, 66.98323, 77L, 79L, 1L, 0L, 86L, 0L,
# 2077L, "female", "afr-amer", 2L, 1L, 3L, 1L, 2L, 59.26457, 56.98883, 67L, 63L, 0L, 0L, 86L, 0L,
# 2078L, "female", "hispanic", 2L, 3L, 4L, 4L, 2L, 66.98323, 63.54885, 79L, 74L, 2L, 0L, 85L, 1L,
# 2079L, "female", "white", 2L, 1L, 3L, 3L, 1L, 32.27546, 50, 20L, 50L, 2L, 0L, 84L, 2L,
# 2080L, "male", "afr-amer", 2L, 3L, 4L, 3L, 3L, 70.94328, 73.72179, 84L, 87L, 0L, 0L, 84L, 1L,
# 2081L, "male", "asian", 2L, 0L, 3L, 4L, 1L, 37.72536, 37.72536, 28L, 28L, 2L, 0L, 81L, 5L,
# 2082L, "female", "white", 2L, 0L, 2L, 1L, 3L, 32.27546, 29.90528, 20L, 17L, 2L, 0L, 83L, 3L,
# 2083L, "male", "white", 2L, 0L, 0L, 2L, 3L, 36.45115, 32.27546, 26L, 20L, 1L, 0L, 85L, 1L,
# 2084L, "female", "asian", 2L, 1L, 3L, 2L, 4L, 64.20476, 71.82729, 75L, 85L, 0L, 0L, 83L, 3L,
# 2085L, "female", "white", 2L, 1L, 4L, 1L, 3L, 56.98883, 71.82729, 63L, 85L, 0L, 0L, 80L, 6L,
# 2086L, "male", "white", 2L, 0L, 4L, 2L, 1L, 44.11754, 24.16932, 39L, 11L, 1L, 0L, 78L, 8L,
# 2087L, "male", "asian", 2L, 0L, 2L, 0L, 3L, 40.15026, 40.15026, 32L, 32L, 1L, 2L, 65L, 21L,
# 2088L, "male", "hispanic", 2L, 0L, 1L, 0L, 1L, 28.17271, 30.72241, 15L, 18L, 1L, 0L, 19L, 1L,
# 2089L, "female", "white", 2L, 2L, 2L, 3L, 2L, 52.64643, 79.59081, 55L, 92L, 0L, 0L, 79L, 7L,
# 2090L, "female", "asian", 2L, 0L, 2L, 3L, 2L, 40.15026, 44.66451, 32L, 40L, 0L, 0L, 81L, 5L,
# 2091L, "male", "asian", 2L, 1L, 4L, 2L, 2L, 41.31353, 40.15026, 34L, 32L, 2L, 4L, 85L, 1L,
# 2092L, "female", "white", 2L, 0L, 2L, 3L, 2L, 59.26457, 89.60951, 67L, 97L, 0L, 0L, 85L, 1L,
# 2093L, "female", "white", 2L, 4L, 4L, 4L, 3L, 45.2079, 46.82059, 41L, 44L, 2L, 0L, 86L, 0L,
# 2094L, "male", "white", 2L, 0L, 2L, 1L, 2L, 45.2079, 53.17941, 41L, 56L, 2L, 0L, 82L, 4L,
# 2095L, "female", "hispanic", 2L, 1L, 4L, 2L, 3L, 38.34572, 55.33549, 29L, 60L, 0L, 0L, 86L, 0L,
# 2096L, "male", "white", 2L, 0L, 3L, 0L, 3L, 46.28556, 55.33549, 43L, 60L, 0L, 0L, 72L, 14L,
# 2097L, "female", "hispanic", 2L, 2L, 2L, 2L, 2L, 65.56011, 51.05624, 77L, 52L, 2L, 3L, 44L, 2L,
# 2098L, "female", "white", 2L, 1L, 3L, 2L, 3L, 51.58518, 65.56011, 53L, 77L, 2L, 0L, 84L, 2L,
# 2099L, "female", "white", 2L, 2L, 4L, 3L, 4L, 46.82059, 68.48849, 44L, 81L, 2L, 0L, 84L, 2L,
# 2100L, "male", "white", 2L, 3L, 3L, 2L, 4L, 50.52795, 43.01117, 51L, 37L, 0L, 0L, 86L, 0L,
# 2101L, "male", "white", 2L, 2L, 3L, 3L, 3L, 59.26457, 55.33549, 67L, 60L, 1L, 1L, 85L, 1L,
# 2102L, "male", "white", 2L, 0L, 2L, 0L, 0L, 49.47205, 43.01117, 49L, 37L, 0L, 0L, 67L, 19L,
# 2103L, "female", "asian", 2L, 1L, 2L, 3L, 2L, 43.01117, 46.82059, 37L, 44L, 0L, 0L, 84L, 2L,
# 2104L, "male", "white", 2L, 1L, 2L, 3L, 3L, 58.11485, 71.82729, 65L, 85L, 0L, 0L, 74L, 11L,
# 2105L, "male", "afr-amer", 2L, 2L, 2L, 3L, 3L, 46.28556, 70.94328, 43L, 84L, 0L, 0L, 86L, 0L,
# 2106L, "female", "hispanic", 2L, 3L, 2L, 3L, 3L, 48.94376, 53.71444, 48L, 57L, 2L, 2L, 81L, 5L,
# 2107L, "female", "afr-amer", 2L, 3L, 3L, 3L, 2L, 98.99289, 56.98883, 99L, 63L, 0L, 0L, 72L, 13L,
# 2108L, "female", "white", 2L, 0L, 2L, 2L, 3L, 41.31353, 50.52795, 34L, 51L, 1L, 0L, 86L, 0L,
# 2109L, "male", "white", 2L, 3L, 4L, 3L, 2L, 73.72179, 82.74353, 87L, 94L, 1L, 0L, 81L, 5L,
# 2110L, "male", "white", 2L, 2L, 1L, 1L, 3L, 64.20476, 65.56011, 75L, 77L, 0L, 0L, 83L, 3L,
# 2111L, "female", "hispanic", 2L, 0L, 1L, 1L, 1L, 53.71444, 51.58518, 57L, 53L, 2L, 2L, 84L, 2L,
# 2112L, "male", "white", 2L, 3L, 2L, 3L, 3L, 55.88246, 98.99289, 61L, 99L, 0L, 0L, 84L, 2L,
# 2113L, "male", "afr-amer", 2L, 0L, 2L, 3L, 1L, 62.90584, 56.98883, 73L, 63L, 0L, 0L, 81L, 5L,
# 2114L, "female", "white", 2L, 3L, 4L, 4L, 4L, 61.04388, 71.82729, 70L, 85L, 1L, 0L, 86L, 0L,
# 2115L, "female", "white", 2L, 4L, 4L, 3L, 4L, 98.99289, 98.99289, 99L, 99L, 0L, 0L, 83L, 3L,
# 2116L, "male", "white", 2L, 2L, 3L, 3L, 2L, 62.90584, 54.7921, 73L, 59L, 2L, 0L, 86L, 0L,
# 2117L, "male", "white", 2L, 2L, 3L, 1L, 2L, 58.68647, 60.44261, 66L, 69L, 0L, 0L, 85L, 1L,
# 2118L, "male", "hispanic", 2L, 2L, 1L, 1L, 0L, 53.71444, 35.12527, 57L, 24L, 3L, 1L, 77L, 9L,
# 2119L, "male", "white", 2L, 3L, 2L, 2L, 1L, 65.56011, 44.11754, 77L, 39L, 0L, 0L, 85L, 1L,
# 2120L, "male", "white", 2L, 1L, 3L, 1L, 3L, 51.58518, 40.15026, 53L, 32L, 3L, 0L, 86L, 0L,
# 2121L, "male", "white", 2L, 0L, 2L, 2L, 3L, 62.90584, 62.27464, 73L, 72L, 0L, 0L, 86L, 0L,
# 2122L, "male", "white", 2L, 3L, 3L, 2L, 2L, 70.94328, 58.11485, 84L, 65L, 1L, 0L, 85L, 1L,
# 2123L, "male", "hispanic", 2L, 0L, 1L, 2L, 0L, 70.09472, 48.41482, 83L, 47L, 0L, 0L, 73L, 12L,
# 2124L, "female", "white", 2L, 1L, 2L, 3L, 3L, 65.56011, 62.27464, 77L, 72L, 0L, 0L, 83L, 3L,
# 2125L, "male", "white", 2L, 2L, 2L, 3L, 3L, 46.82059, 65.56011, 44L, 77L, 2L, 2L, 86L, 0L,
# 2126L, "female", "white", 2L, 3L, 1L, 2L, 2L, 66.98323, 51.58518, 79L, 53L, 0L, 0L, 85L, 1L,
# 2127L, "male", "afr-amer", 2L, 2L, 3L, 3L, 4L, 51.58518, 59.26457, 53L, 67L, 0L, 0L, 81L, 5L,
# 2128L, "female", "white", 2L, 1L, 3L, 3L, 2L, 46.28556, 64.20476, 43L, 75L, 1L, 0L, 85L, 1L,
# 2129L, "male", "white", 2L, 1L, 4L, 3L, 2L, 47.88486, 58.68647, 46L, 66L, 0L, 0L, 85L, 1L,
# 2130L, "female", "hispanic", 2L, 1L, 3L, 3L, 3L, 41.88515, 58.11485, 35L, 65L, 2L, 1L, 78L, 7L,
# 2131L, "female", "white", 2L, 1L, 3L, 4L, 3L, 56.98883, 59.84974, 63L, 68L, 0L, 0L, 80L, 6L,
# 2132L, "female", "white", 2L, 2L, 4L, 2L, 3L, 64.20476, 81.08016, 75L, 93L, 2L, 2L, 86L, 0L,
# 2133L, "female", "white", 2L, 1L, 1L, 2L, 2L, 70.94328, 58.68647, 84L, 66L, 2L, 0L, 78L, 8L,
# 2134L, "male", "hispanic", 2L, 1L, 3L, 0L, 2L, 45.2079, 57.54914, 41L, 64L, 2L, 4L, 86L, 0L,
# 2135L, "female", "white", 2L, 1L, 3L, 2L, 1L, 40.15026, 48.41482, 32L, 47L, 2L, 0L, 84L, 1L,
# 2136L, "male", "hispanic", 2L, 1L, 2L, 2L, 2L, 25.25478, 13.13055, 12L, 4L, 3L, 2L, 86L, 0L,
# 2137L, "male", "white", 2L, 3L, 3L, 3L, 3L, 55.88246, 86.86945, 61L, 96L, 0L, 0L, 82L, 4L,
# 2138L, "female", "asian", 2L, 0L, 1L, 0L, 0L, 98.99289, 93.25195, 99L, 98L, 1L, 0L, 63L, 17L,
# 2139L, "male", "nat-amer", 2L, 2L, 2L, 1L, 2L, 59.26457, 44.11754, 67L, 39L, 0L, 0L, 80L, 6L,
# 2140L, "female", "white", 2L, 1L, 4L, 2L, 3L, 41.88515, 41.31353, 35L, 34L, 1L, 0L, 86L, 0L,
# 2141L, "female", "white", 2L, 4L, 4L, 4L, 4L, 61.04388, 56.98883, 70L, 63L, 2L, 0L, 86L, 0L,
# 2142L, "female", "white", 2L, 2L, 2L, 3L, 2L, 73.72179, 70.94328, 87L, 84L, 0L, 0L, 85L, 1L,
# 2143L, "male", "white", 2L, 3L, 4L, 3L, 2L, 61.04388, 47.88486, 70L, 46L, 2L, 0L, 83L, 3L,
# 2144L, "male", "hispanic", 2L, 0L, 2L, 3L, 2L, 53.71444, 61.04388, 57L, 70L, 1L, 0L, 84L, 1L,
# 2145L, "male", "white", 2L, 2L, 3L, 4L, 3L, 46.82059, 59.26457, 44L, 67L, 1L, 0L, 84L, 2L,
# 2146L, "female", "white", 2L, 1L, 2L, 2L, 1L, 36.45115, 46.82059, 26L, 44L, 3L, 0L, 84L, 2L,
# 2147L, "male", "white", 2L, 0L, 2L, 2L, 3L, 56.98883, 61.04388, 63L, 70L, 0L, 0L, 84L, 2L,
# 2148L, "female", "hispanic", 2L, 0L, 1L, 2L, 0L, 20.40919, 15.35938, 8L, 5L, 2L, 4L, 81L, 5L,
# 2149L, "female", "hispanic", 2L, 0L, 3L, 0L, 3L, 47.88486, 54.7921, 46L, 59L, 1L, 0L, 45L, 41L,
# 2150L, "male", "white", 2L, 2L, 4L, 2L, 2L, 56.98883, 43.01117, 63L, 37L, 2L, 2L, 83L, 3L,
# 2151L, "female", "filipino", 2L, 0L, 2L, 2L, 0L, 54.7921, 71.82729, 59L, 85L, 1L, 0L, 79L, 7L,
# 2152L, "female", "white", 2L, 3L, 3L, 2L, 3L, 47.88486, 69.27759, 46L, 82L, 0L, 0L, 85L, 1L,
# 2153L, "male", "hispanic", 2L, 1L, 2L, 0L, 2L, 36.45115, 47.88486, 26L, 46L, 2L, 0L, 85L, 1L,
# 2154L, "female", "white", 2L, 2L, 3L, 3L, 2L, 66.98323, 68.48849, 79L, 81L, 2L, 0L, 83L, 3L,
# 2155L, "female", "hispanic", 2L, 2L, 3L, 2L, 4L, 54.7921, 53.17941, 59L, 56L, 0L, 0L, 86L, 0L,
# 2156L, "female", "white", 2L, 3L, 3L, 4L, 3L, 76.98948, 69.27759, 90L, 82L, 0L, 0L, 86L, 0L,
# 2157L, "female", "white", 2L, 2L, 2L, 4L, 3L, 65.56011, 70.94328, 77L, 84L, 0L, 0L, 84L, 2L
# )
emilelatour/lamisc documentation built on March 29, 2025, 1:23 p.m.
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Defines functions calc_collin_diag
Documented in calc_collin_diag
#' Calculate Collinearity Diagnostics
#'
#' This function computes collinearity diagnostics, including variance inflation factors (VIF), tolerance, R-squared values, eigenvalues, condition indices, and more. It replicates functionality similar to what is described in the [Stata collinearity diagnostics page](http://www.philender.com/courses/categorical/notes2/collin.html).
#'
#' @param data A data frame containing the variables to analyze.
#' @param ... Variables to include in the analysis, specified without quotes.
#' @param method The method for calculating the correlation matrix. Default is `"pearson"`.
#' @param use How to handle missing values when calculating correlations. Default is `"complete.obs"`.
#' @param method_for_eigen Specifies the method for calculating eigenvalues and condition indices. Options are `"corr"` for the correlation matrix or `"sscp"` for the scaled sum of squares and cross-product matrix. Default is `"corr"`.
#' @param show_inv_cor_mat Logical. If `TRUE`, includes the inverse correlation matrix in the output. Default is `FALSE`.
#'
#' @return A list with the following components:
#' \item{table}{A tibble with the collinearity diagnostics for each variable. Includes VIF, tolerance, R-squared, eigenvalues, and condition indices.}
#' \item{summary}{A tibble summarizing the mean VIF, condition number, and determinant of the correlation matrix.}
#' \item{inv_cor_mat}{The inverse correlation matrix, if `show_inv_cor_mat = TRUE`.}
#'
#' @examples
#' # Example data
#' library(dplyr)
#' # Examples from Phil Ender
#' # http://www.philender.com/courses/categorical/notes2/collin.html
#'
#' hsbdemo <- read.csv("https://stats.idre.ucla.edu/stat/data/hsbdemo.csv")
#' dplyr::glimpse(hsbdemo)
#'
#' calc_collin_diag(data = hsbdemo,
#' female,
#' schtyp,
#' read,
#' write,
#' math,
#' science,
#' socst,
#' method_for_eigen = "corr",
#' method = "pearson")
#'
#'
#' set.seed(123) # Ensure reproducibility
#'
#' n <- 100 # Number of rows
#'
#' lahigh <- tibble(
#' id = 1000 + seq_len(n),
#' gender = sample(c("male", "female"), n, replace = TRUE),
#' ethnic = sample(c("hispanic", "filipino", "afr-amer", "asian", "white"), n, replace = TRUE),
#' school = sample(1:2, n, replace = TRUE),
#' algebra = sample(0:4, n, replace = TRUE),
#' math = sample(0:4, n, replace = TRUE),
#' eng95 = sample(0:4, n, replace = TRUE),
#' eng94 = sample(0:4, n, replace = TRUE),
#' mathnce = runif(n, 1, 100), # Continuous values between 1 and 100
#' langnce = runif(n, 1, 100),
#' mathpr = sample(1:100, n, replace = TRUE), # Integer percentiles
#' langpr = sample(1:100, n, replace = TRUE),
#' biling = sample(0:3, n, replace = TRUE),
#' engprof = sample(0:4, n, replace = TRUE),
#' daysatt = sample(40:90, n, replace = TRUE),
#' daysabs = sample(0:35, n, replace = TRUE)
#' )
#'
#' dplyr::glimpse(lahigh)
#'
#' calc_collin_diag(data = lahigh,
#' mathnce,
#' langnce,
#' mathpr,
#' langpr,
#' method_for_eigen = "corr",
#' method = "pearson")
#'
#' calc_collin_diag(data = lahigh,
#' mathnce,
#' langnce,
#' method_for_eigen = "corr",
#' method = "pearson")
#'
#' @export
#'
#'
calc_collin_diag <- function(data,
...,
method = "pearson",
use = "complete.obs",
method_for_eigen = "corr",
show_inv_cor_mat = FALSE) {
# Fix no visible binding for global variable
variable <- predictors <- form <- r_squared <- vif <- sqrt_vif <- tolerance <- eigenval <- rnk <- cond_index <- NULL
# vars <- rlang::enquos(...)
#### Make sure that all variables are numeric --------------------------------
# data <- data %>%
# dplyr::select(!!! vars) %>%
# mutate_all(.tbl = .,
# .funs = list(~ as.numeric(.)))
data <- data %>%
dplyr::select(...) %>%
mutate(dplyr::across(.cols = dplyr::everything(),
.fns = ~ make_numeric(.)))
vars_names <- names(data)
#### Rsqrd, vif, tolerance --------------------------------
res <- tibble::tibble(
variable = vars_names
) %>%
mutate(predictors = purrr::map(.x = variable,
.f = ~ vars_names[!vars_names %in% .x]),
form = purrr::map2_chr(.x = variable,
.y = predictors,
.f = ~ paste0(.x, " ~ ", paste0(.y, collapse = " + "))),
r_squared = purrr::map_dbl(.x = form,
.f = ~ calc_r_squared(form = .x,
data = data)),
vif = 1 / (1 - r_squared),
sqrt_vif = sqrt(vif),
tolerance = 1 / vif) %>%
dplyr::select(variable,
vif,
sqrt_vif,
tolerance,
r_squared) %>%
{.}
cor_mat <- cor(data,
method = method,
use = use)
#### Eigenvals, Conditional index --------------------------------
## deviation sscp (no intercept) ----------------
# Eigenvalues and condition index computed from correlation matrix without a
# constant.
if (method_for_eigen == "corr") {
svd_x <- svd(cor_mat)
res2 <- tibble::tibble(
variable = colnames(cor_mat),
eigenval = eigen(cor_mat)$values,
cond_index = sqrt(max(svd_x$d) / svd_x$d),
rnk = rank(dplyr::desc(eigenval))
) %>%
dplyr::select(variable, rnk, eigenval, cond_index)
res <- res %>%
dplyr::left_join(.,
res2,
by = "variable")
}
## scaled raw sscp (w/ intercept) ----------------
# By default the eigenvalues and condition index are computed on the scaled
# raw score SSCP matrix with an intercept.
if (method_for_eigen == "sscp") {
sscp <- data %>%
mutate(constant = 1) %>%
as.matrix() %>%
crossprod()
diag_1 <- sscp * diag(ncol(sscp))
diag_1 <- sqrt(diag_1)
diag_1 <- syminv(diag_1)
sscp <- diag_1 %*% sscp %*% diag_1
svd_x <- svd(sscp)
res2 <- tibble::tibble(
variable = c(colnames(data), "Intercept"),
eigenval = eigen(sscp)$values,
cond_index = sqrt(max(svd_x$d) / svd_x$d),
rnk = rank(dplyr::desc(eigenval))
) %>%
dplyr::select(variable, rnk, eigenval, cond_index)
res <- res %>%
dplyr::bind_rows(.,
tibble::tibble(variable = "Intercept",
vif = NA_real_,
sqrt_vif = NA_real_,
tolerance = NA_real_,
r_squared = NA_real_)) %>%
dplyr::left_join(.,
res2,
by = "variable")
}
#### Summary results --------------------------------
summary_res <- tibble::tibble(
info = c("Mean VIF",
"Condition Number",
"Determinant of Correlation Matrix"),
rstls = c(mean(res$vif, na.rm = TRUE),
max(res$cond_index),
det(cor_mat))
)
results <- list(table = res,
summary = summary_res)
#### Inverse correlation matrix --------------------------------
if (show_inv_cor_mat == TRUE) {
inv_cor_mat <- cor_mat %>%
solve(.) %>%
round(.,
digits = 5)
results <- list(table = res,
summary = summary_res,
inv_cor_mat = inv_cor_mat)
}
#### End of function --------------------------------
return(results)
}
#' Calculate R-Squared Value
#'
#' This helper function computes the R-squared value for a given formula and dataset.
#'
#' @param form A formula specifying the regression model (e.g., `"y ~ x1 + x2"`).
#' @param data A data frame containing the variables used in the formula.
#'
#' @importFrom stats lm
#'
#' @return The R-squared value from the linear model.
#'
#' @examples
#' data <- mtcars
#' form <- "mpg ~ disp + hp + wt"
#' calc_r_squared(form, data)
#'
#' @export
calc_r_squared <- function(form, data) {
# One way - old version
# mod1 <- glm(as.formula(form),
# data = data,
# family = gaussian(link = "identity"))
#
# # rsq::rsq(mod1)
# with(summary(mod1), 1 - deviance/null.deviance)
# Another way
# mod1 <- lm(as.formula(form),
# data = data)
#
# summary(mod1)$r.squared
# Manual method
# Fit the model
model <- lm(as.formula(form), data = data)
y <- purrr::pluck(model, "model", 1)
# Predicted values
y_pred <- predict(model)
# Residual sum of squares (SSR)
ssr <- sum((y - y_pred)^2)
# Total sum of squares (SST)
sst <- sum((y - mean(y))^2)
# R-squared
r_squared_manual <- 1 - (ssr / sst)
return(r_squared_manual)
}
#' Symmetric Inverse
#'
#' Computes the inverse of a symmetric positive-definite matrix using its Cholesky decomposition.
#'
#' @param x A symmetric positive-definite matrix.
#'
#' @return The inverse of the input matrix.
#'
#' @examples
#' mat <- matrix(c(4, 2, 2, 3), ncol = 2)
#' syminv(mat)
#'
#' @export
syminv <- function(x) {
# https://rdrr.io/cran/MNM/src/R/syminv.R
# http://www.philender.com/courses/multivariate/notes/magic.html
ch_x <- chol(x)
chol2inv(ch_x)
}
#' Convert a Column to Numeric Codes
#'
#' This function converts a character or factor column into numeric codes, preserving numeric columns as-is. Character and factor variables are first converted to factors and then assigned numeric codes based on their levels.
#'
#' @param col A vector (column) to be converted. It can be a character, factor, or numeric vector.
#'
#' @return A numeric vector. If the input is a character or factor column, it is converted to numeric codes. Numeric columns are returned unchanged.
#'
#' @examples
#' # Example usage
#' char_col <- c("a", "b", "a", "c")
#' factor_col <- factor(c("low", "medium", "high"))
#' numeric_col <- c(1.2, 3.4, 5.6)
#'
#' # Convert columns to numeric codes
#' make_numeric(char_col) # Returns numeric codes for characters
#' make_numeric(factor_col) # Returns numeric codes for factors
#' make_numeric(numeric_col) # Returns numeric values unchanged
#'
#' @export
make_numeric <- function(col) {
if (is.character(col) || is.factor(col)) {
as.numeric(as.factor(col)) # Convert characters or factors to numeric codes
} else {
col # Leave numeric columns as is
}
}
# lahigh <- tibble::tribble(
# ~id, ~gender, ~ethnic, ~school, ~algebra, ~math, ~eng95, ~eng94, ~mathnce, ~langnce, ~mathpr, ~langpr, ~biling, ~engprof, ~daysatt, ~daysabs,
# 1001L, "male", "hispanic", 1L, 3L, 0L, 2L, 2L, 56.98883, 42.45086, 63L, 36L, 2L, 2L, 73L, 4L,
# 1002L, "male", "hispanic", 1L, 1L, 2L, 2L, 4L, 37.09416, 46.82059, 27L, 44L, 2L, 3L, 73L, 4L,
# 1003L, "female", "hispanic", 1L, 3L, 3L, 4L, 3L, 32.27546, 43.56657, 20L, 38L, 2L, 3L, 76L, 2L,
# 1004L, "female", "hispanic", 1L, 1L, 4L, 3L, 4L, 29.05672, 43.56657, 16L, 38L, 2L, 2L, 74L, 3L,
# 1005L, "female", "hispanic", 1L, 0L, 1L, 0L, 2L, 6.748048, 27.24847, 2L, 14L, 3L, 1L, 73L, 3L,
# 1006L, "female", "hispanic", 1L, 4L, 1L, 3L, 4L, 61.65428, 48.41482, 71L, 47L, 0L, 1L, 62L, 13L,
# 1007L, "female", "hispanic", 1L, 0L, 1L, 1L, 3L, 56.98883, 40.73543, 63L, 33L, 2L, 2L, 66L, 11L,
# 1008L, "male", "hispanic", 1L, 0L, 0L, 0L, 0L, 10.39049, 15.35938, 3L, 5L, 2L, 1L, 72L, 7L,
# 1009L, "male", "hispanic", 1L, 2L, 2L, 3L, 2L, 50.52795, 52.11514, 51L, 54L, 2L, 1L, 63L, 10L,
# 1010L, "male", "filipino", 1L, 0L, 2L, 0L, 1L, 49.47205, 42.45086, 49L, 36L, 0L, 0L, 68L, 9L,
# 1011L, "female", "filipino", 1L, 1L, 0L, 1L, 1L, 39.55739, 36.45115, 31L, 26L, 0L, 0L, 72L, 4L,
# 1012L, "male", "hispanic", 1L, 4L, 4L, 3L, 4L, 33.73761, 13.13055, 22L, 4L, 2L, 2L, 74L, 5L,
# 1013L, "female", "hispanic", 1L, 3L, 4L, 3L, 3L, 62.90584, 62.27464, 73L, 72L, 2L, 2L, 72L, 5L,
# 1014L, "female", "afr-amer", 1L, 0L, 2L, 2L, 3L, 65.56011, 44.66451, 77L, 40L, 0L, 0L, 74L, 3L,
# 1015L, "male", "filipino", 1L, 0L, 3L, 1L, 1L, 23.01052, 25.25478, 10L, 12L, 1L, 0L, 76L, 1L,
# 1016L, "male", "hispanic", 1L, 4L, 3L, 4L, 2L, 75.83068, 61.04388, 89L, 70L, 2L, 2L, 76L, 0L,
# 1017L, "female", "hispanic", 1L, 2L, 2L, 4L, 4L, 41.31353, 49.47205, 34L, 49L, 2L, 1L, 75L, 1L,
# 1018L, "female", "hispanic", 1L, 0L, 2L, 4L, 3L, 41.88515, 65.56011, 35L, 77L, 2L, 1L, 74L, 0L,
# 1019L, "male", "afr-amer", 1L, 1L, 2L, 2L, 1L, 65.56011, 46.82059, 77L, 44L, 1L, 0L, 75L, 2L,
# 1020L, "male", "hispanic", 1L, 3L, 0L, 0L, 0L, 13.13055, 6.748048, 4L, 2L, 3L, 2L, 55L, 24L,
# 1021L, "female", "hispanic", 1L, 0L, 1L, 3L, 2L, 33.01677, 42.45086, 21L, 36L, 2L, 3L, 75L, 2L,
# 1022L, "male", "hispanic", 1L, 0L, 2L, 2L, 2L, 55.88246, 64.87473, 61L, 76L, 2L, 1L, 76L, 0L,
# 1023L, "male", "hispanic", 1L, 3L, 4L, 3L, 3L, 45.2079, 55.33549, 41L, 60L, 2L, 1L, 76L, 1L,
# 1024L, "male", "hispanic", 1L, 2L, 2L, 2L, 2L, 56.98883, 44.66451, 63L, 40L, 2L, 2L, 76L, 0L,
# 1025L, "female", "hispanic", 1L, 3L, 4L, 4L, 3L, 31.5115, 38.34572, 19L, 29L, 2L, 1L, 71L, 8L,
# 1026L, "male", "afr-amer", 1L, 0L, 2L, 3L, 3L, 52.64643, 50, 55L, 50L, 0L, 0L, 67L, 3L,
# 1027L, "male", "hispanic", 1L, 0L, 1L, 0L, 2L, 17.25647, 6.748048, 6L, 2L, 0L, 0L, 70L, 7L,
# 1028L, "female", "hispanic", 1L, 0L, 2L, 1L, 2L, 33.01677, 40.15026, 21L, 32L, 2L, 2L, 76L, 0L,
# 1029L, "male", "hispanic", 1L, 3L, 1L, 2L, 2L, 61.04388, 57.54914, 70L, 64L, 1L, 1L, 74L, 2L,
# 1030L, "male", "afr-amer", 1L, 1L, 4L, 2L, 3L, 66.98323, 71.82729, 79L, 85L, 0L, 0L, 77L, 0L,
# 1031L, "male", "hispanic", 1L, 1L, 1L, 1L, 1L, 1.007114, 45.2079, 1L, 41L, 1L, 4L, 77L, 0L,
# 1032L, "female", "hispanic", 1L, 1L, 4L, 2L, 3L, 38.34572, 35.12527, 29L, 24L, 3L, 1L, 76L, 1L,
# 1033L, "male", "hispanic", 1L, 1L, 3L, 3L, 1L, 44.66451, 46.82059, 40L, 44L, 2L, 2L, 32L, 3L,
# 1034L, "male", "asian", 1L, 2L, 4L, 3L, 2L, 44.11754, 46.82059, 39L, 44L, 3L, 2L, 77L, 0L,
# 1035L, "male", "hispanic", 1L, 2L, 3L, 2L, 0L, 59.84974, 46.28556, 68L, 43L, 3L, 2L, 77L, 0L,
# 1036L, "female", "hispanic", 1L, 0L, 4L, 0L, 3L, 32.27546, 47.35357, 20L, 45L, 3L, 1L, 49L, 28L,
# 1037L, "male", "hispanic", 1L, 0L, 0L, 2L, 1L, 23.01052, 49.47205, 10L, 49L, 1L, 0L, 71L, 8L,
# 1038L, "male", "hispanic", 1L, 2L, 2L, 3L, 3L, 70.94328, 61.04388, 84L, 70L, 2L, 4L, 72L, 5L,
# 1039L, "male", "afr-amer", 1L, 0L, 2L, 1L, 0L, 1.007114, 1.007114, 1L, 1L, 0L, 0L, 75L, 2L,
# 1040L, "female", "hispanic", 1L, 0L, 0L, 1L, 0L, 41.88515, 52.11514, 35L, 54L, 3L, 2L, 46L, 27L,
# 1041L, "female", "hispanic", 1L, 3L, 3L, 3L, 4L, 40.15026, 35.12527, 32L, 24L, 2L, 2L, 72L, 5L,
# 1042L, "female", "hispanic", 1L, 0L, 1L, 0L, 2L, 41.31353, 38.34572, 34L, 29L, 3L, 2L, 59L, 18L,
# 1043L, "female", "hispanic", 1L, 0L, 4L, 2L, 3L, 44.66451, 58.68647, 40L, 66L, 3L, 0L, 57L, 19L,
# 1044L, "male", "hispanic", 1L, 1L, 2L, 1L, 1L, 38.34572, 42.45086, 29L, 36L, 2L, 2L, 67L, 9L,
# 1045L, "male", "hispanic", 1L, 2L, 3L, 0L, 0L, 32.27546, 1.007114, 20L, 1L, 1L, 2L, 68L, 9L,
# 1046L, "female", "hispanic", 1L, 3L, 4L, 3L, 1L, 37.09416, 32.27546, 27L, 20L, 0L, 1L, 75L, 4L,
# 1047L, "male", "hispanic", 1L, 2L, 2L, 2L, 0L, 63.54885, 57.54914, 74L, 64L, 2L, 1L, 75L, 2L,
# 1048L, "male", "hispanic", 1L, 1L, 2L, 2L, 2L, 43.56657, 41.31353, 38L, 34L, 1L, 1L, 68L, 3L,
# 1049L, "male", "hispanic", 1L, 0L, 0L, 2L, 0L, 33.01677, 24.16932, 21L, 11L, 0L, 1L, 68L, 9L,
# 1050L, "female", "asian", 1L, 0L, 0L, 0L, 3L, 68.48849, 59.26457, 81L, 67L, 2L, 1L, 56L, 20L,
# 1051L, "male", "hispanic", 1L, 0L, 3L, 0L, 2L, 29.05672, 21.7637, 16L, 9L, 1L, 0L, 65L, 6L,
# 1052L, "male", "asian", 1L, 4L, 2L, 4L, 2L, 54.7921, 54.7921, 59L, 59L, 0L, 1L, 76L, 0L,
# 1053L, "male", "hispanic", 1L, 0L, 0L, 0L, 2L, 48.94376, 51.58518, 48L, 53L, 2L, 1L, 50L, 27L,
# 1054L, "female", "hispanic", 1L, 2L, 4L, 2L, 3L, 52.64643, 50.52795, 55L, 51L, 2L, 1L, 65L, 12L,
# 1055L, "female", "hispanic", 1L, 0L, 0L, 0L, 0L, 13.13055, 32.27546, 4L, 20L, 3L, 1L, 43L, 34L,
# 1056L, "male", "asian", 1L, 3L, 0L, 2L, 0L, 53.71444, 41.88515, 57L, 35L, 1L, 4L, 76L, 1L,
# 1057L, "male", "afr-amer", 1L, 1L, 0L, 1L, 1L, 15.35938, 32.27546, 5L, 20L, 0L, 0L, 52L, 25L,
# 1058L, "male", "afr-amer", 1L, 0L, 2L, 0L, 0L, 10.39049, 17.25647, 3L, 6L, 0L, 0L, 71L, 5L,
# 1059L, "female", "hispanic", 1L, 1L, 2L, 2L, 3L, 34.43988, 38.34572, 23L, 29L, 3L, 3L, 74L, 3L,
# 1060L, "female", "hispanic", 1L, 3L, 2L, 4L, 2L, 41.88515, 42.45086, 35L, 36L, 1L, 1L, 77L, 2L,
# 1061L, "male", "hispanic", 1L, 0L, 0L, 1L, 1L, 40.73543, 55.33549, 33L, 60L, 3L, 2L, 76L, 1L,
# 1062L, "female", "hispanic", 1L, 1L, 1L, 2L, 1L, 37.09416, 52.64643, 27L, 55L, 2L, 2L, 70L, 7L,
# 1063L, "male", "hispanic", 1L, 1L, 2L, 3L, 3L, 26.2782, 26.2782, 13L, 13L, 1L, 1L, 73L, 4L,
# 1064L, "male", "hispanic", 1L, 2L, 0L, 3L, 1L, 47.88486, 36.45115, 46L, 26L, 3L, 1L, 71L, 8L,
# 1065L, "female", "hispanic", 1L, 0L, 0L, 1L, 0L, 38.95612, 55.88246, 30L, 61L, 0L, 0L, 71L, 6L,
# 1066L, "male", "asian", 1L, 0L, 0L, 0L, 1L, 40.15026, 47.35357, 32L, 45L, 0L, 0L, 61L, 16L,
# 1067L, "female", "afr-amer", 1L, 0L, 1L, 3L, 2L, 36.45115, 40.15026, 26L, 32L, 0L, 0L, 74L, 3L,
# 1068L, "female", "hispanic", 1L, 0L, 2L, 1L, 2L, 27.24847, 39.55739, 14L, 31L, 1L, 2L, 71L, 4L,
# 1069L, "female", "filipino", 1L, 1L, 3L, 3L, 3L, 39.55739, 43.56657, 31L, 38L, 1L, 0L, 73L, 3L,
# 1070L, "female", "hispanic", 1L, 0L, 2L, 1L, 1L, 48.94376, 36.45115, 48L, 26L, 3L, 3L, 72L, 5L,
# 1071L, "male", "hispanic", 1L, 2L, 3L, 3L, 2L, 62.27464, 46.28556, 72L, 43L, 1L, 0L, 73L, 0L,
# 1072L, "male", "hispanic", 1L, 2L, 3L, 2L, 3L, 66.98323, 59.84974, 79L, 68L, 0L, 1L, 67L, 9L,
# 1073L, "male", "filipino", 1L, 2L, 2L, 3L, 3L, 28.17271, 59.84974, 15L, 68L, 3L, 0L, 77L, 0L,
# 1074L, "male", "hispanic", 1L, 0L, 0L, 0L, 0L, 35.12527, 37.09416, 24L, 27L, 1L, 1L, 69L, 8L,
# 1075L, "female", "filipino", 1L, 3L, 4L, 4L, 3L, 52.64643, 70.09472, 55L, 83L, 0L, 0L, 77L, 0L,
# 1076L, "female", "afr-amer", 1L, 0L, 3L, 3L, 3L, 26.2782, 35.12527, 13L, 24L, 0L, 0L, 65L, 11L,
# 1077L, "male", "hispanic", 1L, 3L, 4L, 1L, 3L, 41.31353, 42.45086, 34L, 36L, 0L, 1L, 75L, 4L,
# 1078L, "male", "hispanic", 1L, 2L, 1L, 2L, 2L, 59.26457, 71.82729, 67L, 85L, 1L, 1L, 75L, 2L,
# 1079L, "male", "hispanic", 1L, 0L, 0L, 0L, 0L, 1.007114, 17.25647, 1L, 6L, 3L, 1L, 35L, 35L,
# 1080L, "female", "hispanic", 1L, 0L, 0L, 0L, 2L, 33.01677, 41.88515, 21L, 35L, 3L, 0L, 54L, 23L,
# 1081L, "female", "hispanic", 1L, 0L, 4L, 0L, 3L, 40.73543, 42.45086, 33L, 36L, 3L, 2L, 64L, 13L,
# 1082L, "male", "hispanic", 1L, 2L, 4L, 2L, 4L, 66.26239, 64.87473, 78L, 76L, 0L, 1L, 71L, 6L,
# 1083L, "female", "afr-amer", 1L, 4L, 2L, 3L, 2L, 70.94328, 45.74812, 84L, 42L, 0L, 0L, 79L, 0L,
# 1084L, "male", "hispanic", 1L, 2L, 0L, 3L, 1L, 54.7921, 60.44261, 59L, 69L, 2L, 2L, 71L, 6L,
# 1085L, "male", "hispanic", 1L, 3L, 1L, 2L, 2L, 64.20476, 50.52795, 75L, 51L, 2L, 1L, 77L, 0L,
# 1086L, "male", "afr-amer", 1L, 1L, 2L, 2L, 1L, 33.73761, 40.15026, 22L, 32L, 0L, 0L, 66L, 8L,
# 1087L, "female", "hispanic", 1L, 0L, 3L, 1L, 2L, 49.47205, 44.66451, 49L, 40L, 0L, 0L, 66L, 11L,
# 1088L, "female", "hispanic", 1L, 0L, 3L, 4L, 2L, 26.2782, 73.72179, 13L, 87L, 2L, 1L, 66L, 11L,
# 1089L, "male", "filipino", 1L, 4L, 3L, 4L, 3L, 70.94328, 54.25188, 84L, 58L, 1L, 3L, 73L, 4L,
# 1090L, "male", "hispanic", 1L, 0L, 0L, 0L, 1L, 37.09416, 41.31353, 27L, 34L, 2L, 2L, 71L, 6L,
# 1091L, "female", "hispanic", 1L, 1L, 4L, 2L, 4L, 37.09416, 49.47205, 27L, 49L, 0L, 3L, 54L, 23L,
# 1092L, "female", "hispanic", 1L, 3L, 2L, 2L, 2L, 61.04388, 69.27759, 70L, 82L, 1L, 1L, 72L, 5L,
# 1093L, "male", "hispanic", 1L, 1L, 3L, 4L, 2L, 86.86945, 86.86945, 96L, 96L, 2L, 2L, 72L, 5L,
# 1094L, "female", "afr-amer", 1L, 0L, 0L, 0L, 0L, 61.04388, 64.20476, 70L, 75L, 0L, 0L, 51L, 26L,
# 1095L, "female", "hispanic", 1L, 0L, 2L, 3L, 4L, 23.01052, 6.748048, 10L, 2L, 3L, 3L, 69L, 7L,
# 1096L, "male", "hispanic", 1L, 0L, 1L, 0L, 2L, 27.24847, 35.12527, 14L, 24L, 3L, 1L, 76L, 1L,
# 1097L, "male", "hispanic", 1L, 0L, 1L, 3L, 2L, 32.27546, 46.82059, 20L, 44L, 2L, 2L, 68L, 9L,
# 1098L, "male", "hispanic", 1L, 0L, 0L, 0L, 0L, 24.16932, 17.25647, 11L, 6L, 2L, 2L, 66L, 11L,
# 1099L, "male", "hispanic", 1L, 0L, 2L, 0L, 0L, 45.74812, 50, 42L, 50L, 2L, 1L, 60L, 18L,
# 1100L, "male", "hispanic", 1L, 0L, 1L, 0L, 0L, 6.748048, 13.13055, 2L, 4L, 3L, 2L, 56L, 12L,
# 1101L, "male", "afr-amer", 1L, 0L, 0L, 0L, 0L, 35.12527, 27.24847, 24L, 14L, 0L, 0L, 73L, 3L,
# 1102L, "male", "asian", 1L, 0L, 3L, 1L, 3L, 43.01117, 28.17271, 37L, 15L, 3L, 0L, 69L, 0L,
# 1103L, "male", "hispanic", 1L, 0L, 0L, 2L, 0L, 26.2782, 13.13055, 13L, 4L, 3L, 1L, 73L, 4L,
# 1104L, "male", "hispanic", 1L, 2L, 1L, 1L, 1L, 10.39049, 29.05672, 3L, 16L, 3L, 0L, 68L, 10L,
# 1105L, "male", "afr-amer", 1L, 1L, 3L, 2L, 4L, 61.04388, 66.26239, 70L, 78L, 0L, 0L, 61L, 16L,
# 1106L, "female", "hispanic", 1L, 1L, 1L, 2L, 3L, 37.09416, 51.58518, 27L, 53L, 2L, 2L, 74L, 1L,
# 1107L, "female", "afr-amer", 1L, 0L, 2L, 4L, 1L, 1.007114, 1.007114, 1L, 1L, 0L, 0L, 70L, 9L,
# 1108L, "female", "asian", 1L, 1L, 4L, 3L, 3L, 55.88246, 45.2079, 61L, 41L, 2L, 0L, 74L, 3L,
# 1109L, "male", "hispanic", 1L, 3L, 3L, 3L, 3L, 46.82059, 38.34572, 44L, 29L, 3L, 3L, 77L, 0L,
# 1110L, "male", "hispanic", 1L, 0L, 0L, 0L, 0L, 41.88515, 56.98883, 35L, 63L, 2L, 3L, 68L, 9L,
# 1111L, "male", "asian", 1L, 3L, 0L, 2L, 2L, 66.26239, 35.79525, 78L, 25L, 3L, 0L, 65L, 14L,
# 1112L, "female", "hispanic", 1L, 0L, 3L, 2L, 2L, 10.39049, 38.95612, 3L, 30L, 2L, 2L, 70L, 7L,
# 1113L, "male", "hispanic", 1L, 0L, 1L, 0L, 1L, 33.01677, 40.15026, 21L, 32L, 3L, 4L, 74L, 3L,
# 1114L, "male", "hispanic", 1L, 0L, 0L, 3L, 4L, 36.45115, 20.40919, 26L, 8L, 3L, 3L, 67L, 10L,
# 1115L, "male", "hispanic", 1L, 0L, 3L, 2L, 2L, 46.82059, 65.56011, 44L, 77L, 2L, 1L, 64L, 12L,
# 1116L, "female", "hispanic", 1L, 2L, 1L, 2L, 0L, 48.41482, 34.43988, 47L, 23L, 1L, 0L, 71L, 6L,
# 1117L, "female", "hispanic", 1L, 0L, 0L, 1L, 2L, 41.88515, 41.88515, 35L, 35L, 2L, 0L, 42L, 35L,
# 1118L, "female", "afr-amer", 1L, 3L, 3L, 4L, 3L, 20.40919, 25.25478, 8L, 12L, 0L, 0L, 64L, 13L,
# 1119L, "female", "hispanic", 1L, 3L, 1L, 4L, 3L, 73.72179, 74.74522, 87L, 88L, 2L, 1L, 74L, 3L,
# 1120L, "male", "hispanic", 1L, 0L, 2L, 3L, 2L, 10.39049, 40.15026, 3L, 32L, 3L, 2L, 65L, 10L,
# 1121L, "male", "hispanic", 1L, 0L, 0L, 1L, 2L, 17.25647, 20.40919, 6L, 8L, 3L, 3L, 71L, 6L,
# 1122L, "male", "afr-amer", 1L, 4L, 3L, 4L, 3L, 75.83068, 64.87473, 89L, 76L, 0L, 0L, 76L, 0L,
# 1123L, "male", "hispanic", 1L, 1L, 1L, 1L, 0L, 26.2782, 23.01052, 13L, 10L, 3L, 1L, 75L, 2L,
# 1124L, "male", "hispanic", 1L, 0L, 3L, 3L, 4L, 70.94328, 82.74353, 84L, 94L, 2L, 1L, 71L, 6L,
# 1125L, "male", "hispanic", 1L, 4L, 4L, 2L, 2L, 76.98948, 68.48849, 90L, 81L, 1L, 0L, 72L, 5L,
# 1126L, "female", "hispanic", 1L, 1L, 4L, 3L, 4L, 61.65428, 58.11485, 71L, 65L, 2L, 2L, 62L, 13L,
# 1127L, "female", "afr-amer", 1L, 0L, 0L, 2L, 1L, 28.17271, 6.748048, 15L, 2L, 0L, 0L, 73L, 4L,
# 1128L, "female", "hispanic", 1L, 0L, 2L, 0L, 2L, 45.2079, 48.94376, 41L, 48L, 2L, 1L, 72L, 5L,
# 1129L, "female", "asian", 1L, 4L, 3L, 4L, 3L, 56.98883, 65.56011, 63L, 77L, 0L, 0L, 74L, 3L,
# 1130L, "female", "hispanic", 1L, 0L, 1L, 0L, 1L, 41.31353, 48.94376, 34L, 48L, 2L, 2L, 44L, 30L,
# 1131L, "female", "hispanic", 1L, 0L, 1L, 1L, 1L, 47.35357, 46.82059, 45L, 44L, 0L, 2L, 61L, 16L,
# 1132L, "female", "hispanic", 1L, 1L, 0L, 0L, 1L, 38.34572, 43.01117, 29L, 37L, 0L, 2L, 62L, 15L,
# 1133L, "female", "hispanic", 1L, 1L, 2L, 1L, 0L, 10.39049, 6.748048, 3L, 2L, 3L, 2L, 65L, 12L,
# 1134L, "male", "hispanic", 1L, 3L, 0L, 4L, 1L, 41.88515, 36.45115, 35L, 26L, 2L, 4L, 78L, 1L,
# 1135L, "male", "afr-amer", 1L, 1L, 2L, 3L, 2L, 40.15026, 38.95612, 32L, 30L, 0L, 0L, 72L, 1L,
# 1136L, "male", "hispanic", 1L, 0L, 3L, 2L, 2L, 33.73761, 35.79525, 22L, 25L, 0L, 0L, 70L, 7L,
# 1137L, "female", "hispanic", 1L, 4L, 1L, 4L, 4L, 68.48849, 52.64643, 81L, 55L, 1L, 2L, 74L, 1L,
# 1138L, "female", "asian", 1L, 0L, 2L, 0L, 3L, 98.99289, 64.20476, 99L, 75L, 2L, 2L, 13L, 45L,
# 1139L, "female", "hispanic", 1L, 4L, 2L, 3L, 4L, 62.90584, 43.01117, 73L, 37L, 2L, 3L, 69L, 10L,
# 1140L, "male", "asian", 1L, 3L, 3L, 3L, 3L, 60.44261, 36.45115, 69L, 26L, 2L, 4L, 74L, 3L,
# 1141L, "female", "afr-amer", 1L, 1L, 0L, 2L, 1L, 37.09416, 10.39049, 27L, 3L, 0L, 0L, 52L, 27L,
# 1142L, "female", "hispanic", 1L, 2L, 1L, 2L, 2L, 26.2782, 33.01677, 13L, 21L, 2L, 2L, 74L, 2L,
# 1143L, "female", "hispanic", 1L, 0L, 0L, 1L, 1L, 64.87473, 53.71444, 76L, 57L, 2L, 1L, 58L, 13L,
# 1144L, "female", "afr-amer", 1L, 0L, 2L, 3L, 2L, 18.91984, 29.05672, 7L, 16L, 0L, 0L, 70L, 2L,
# 1145L, "male", "hispanic", 1L, 0L, 2L, 0L, 2L, 54.7921, 47.88486, 59L, 46L, 2L, 1L, 74L, 5L,
# 1146L, "female", "hispanic", 1L, 0L, 2L, 2L, 4L, 38.34572, 38.95612, 29L, 30L, 2L, 1L, 64L, 5L,
# 1147L, "female", "hispanic", 1L, 0L, 4L, 1L, 4L, 53.71444, 52.11514, 57L, 54L, 2L, 2L, 69L, 4L,
# 1148L, "female", "hispanic", 1L, 3L, 0L, 4L, 3L, 46.82059, 51.58518, 44L, 53L, 1L, 3L, 76L, 3L,
# 1149L, "female", "hispanic", 1L, 0L, 3L, 3L, 3L, 51.58518, 71.82729, 53L, 85L, 1L, 1L, 44L, 20L,
# 1150L, "female", "hispanic", 1L, 0L, 1L, 1L, 2L, 34.43988, 40.15026, 23L, 32L, 3L, 1L, 63L, 12L,
# 1151L, "female", "afr-amer", 1L, 2L, 0L, 4L, 0L, 38.34572, 44.66451, 29L, 40L, 0L, 0L, 48L, 31L,
# 1152L, "male", "asian", 1L, 0L, 2L, 2L, 2L, 44.66451, 40.73543, 40L, 33L, 3L, 0L, 70L, 6L,
# 1153L, "male", "hispanic", 1L, 0L, 4L, 2L, 0L, 49.47205, 31.5115, 49L, 19L, 2L, 3L, 63L, 14L,
# 1154L, "female", "afr-amer", 1L, 0L, 3L, 0L, 3L, 43.56657, 46.82059, 38L, 44L, 0L, 0L, 56L, 13L,
# 1155L, "male", "afr-amer", 1L, 0L, 2L, 3L, 4L, 39.55739, 49.47205, 31L, 49L, 0L, 0L, 71L, 6L,
# 1156L, "female", "afr-amer", 1L, 0L, 0L, 0L, 0L, 33.01677, 47.35357, 21L, 45L, 0L, 0L, 65L, 12L,
# 1157L, "male", "afr-amer", 1L, 0L, 2L, 0L, 0L, 20.40919, 29.05672, 8L, 16L, 0L, 0L, 65L, 12L,
# 1158L, "male", "hispanic", 1L, 3L, 0L, 2L, 3L, 43.01117, 34.43988, 37L, 23L, 3L, 3L, 77L, 0L,
# 1159L, "male", "hispanic", 1L, 3L, 4L, 4L, 3L, 51.58518, 43.56657, 53L, 38L, 2L, 1L, 78L, 1L,
# 2001L, "female", "white", 2L, 0L, 1L, 0L, 3L, 39.55739, 50.52795, 31L, 51L, 0L, 0L, 82L, 4L,
# 2002L, "male", "white", 2L, 2L, 1L, 2L, 1L, 53.71444, 1.007114, 57L, 1L, 3L, 0L, 86L, 0L,
# 2003L, "male", "filipino", 2L, 1L, 2L, 2L, 1L, 53.71444, 38.95612, 57L, 30L, 0L, 0L, 86L, 0L,
# 2004L, "male", "white", 2L, 1L, 2L, 2L, 3L, 54.7921, 64.20476, 59L, 75L, 1L, 0L, 84L, 2L,
# 2005L, "female", "white", 2L, 1L, 2L, 1L, 2L, 38.34572, 54.7921, 29L, 59L, 0L, 0L, 85L, 1L,
# 2006L, "female", "asian", 2L, 2L, 3L, 4L, 3L, 45.2079, 71.82729, 41L, 85L, 1L, 0L, 84L, 2L,
# 2007L, "male", "white", 2L, 2L, 3L, 3L, 2L, 61.65428, 58.68647, 71L, 66L, 0L, 0L, 86L, 0L,
# 2008L, "female", "white", 2L, 1L, 2L, 2L, 2L, 54.7921, 50, 59L, 50L, 3L, 0L, 86L, 0L,
# 2009L, "male", "white", 2L, 1L, 3L, 2L, 4L, 61.65428, 54.7921, 71L, 59L, 0L, 0L, 86L, 0L,
# 2010L, "female", "white", 2L, 1L, 4L, 3L, 2L, 61.04388, 58.68647, 70L, 66L, 0L, 0L, 79L, 7L,
# 2011L, "male", "white", 2L, 3L, 3L, 3L, 1L, 65.56011, 66.26239, 77L, 78L, 1L, 0L, 84L, 2L,
# 2012L, "female", "asian", 2L, 1L, 1L, 2L, 3L, 61.04388, 71.82729, 70L, 85L, 1L, 0L, 76L, 9L,
# 2013L, "female", "white", 2L, 1L, 4L, 3L, 3L, 73.72179, 55.33549, 87L, 60L, 2L, 0L, 80L, 6L,
# 2014L, "male", "white", 2L, 0L, 3L, 4L, 0L, 54.7921, 51.58518, 59L, 53L, 0L, 0L, 82L, 4L,
# 2015L, "male", "white", 2L, 1L, 3L, 2L, 2L, 58.11485, 58.11485, 65L, 65L, 0L, 0L, 85L, 1L,
# 2016L, "female", "hispanic", 2L, 1L, 3L, 2L, 3L, 37.72536, 46.82059, 28L, 44L, 2L, 3L, 79L, 7L,
# 2017L, "male", "white", 2L, 3L, 3L, 3L, 3L, 65.56011, 70.09472, 77L, 83L, 1L, 0L, 86L, 0L,
# 2018L, "male", "white", 2L, 3L, 2L, 3L, 3L, 58.11485, 68.48849, 65L, 81L, 1L, 0L, 86L, 0L,
# 2019L, "female", "white", 2L, 2L, 2L, 4L, 4L, 62.90584, 71.82729, 73L, 85L, 0L, 0L, 82L, 4L,
# 2020L, "male", "hispanic", 2L, 3L, 2L, 3L, 2L, 98.99289, 55.33549, 99L, 60L, 0L, 0L, 82L, 2L,
# 2021L, "female", "white", 2L, 3L, 3L, 4L, 3L, 53.71444, 66.98323, 57L, 79L, 2L, 2L, 86L, 0L,
# 2022L, "female", "white", 2L, 3L, 1L, 3L, 2L, 65.56011, 50, 77L, 50L, 0L, 0L, 82L, 4L,
# 2023L, "female", "hispanic", 2L, 3L, 2L, 4L, 2L, 53.71444, 65.56011, 57L, 77L, 0L, 0L, 84L, 2L,
# 2024L, "female", "afr-amer", 2L, 0L, 0L, 0L, 2L, 48.41482, 29.05672, 47L, 16L, 0L, 0L, 67L, 18L,
# 2025L, "female", "white", 2L, 0L, 3L, 3L, 3L, 35.12527, 52.11514, 24L, 54L, 2L, 0L, 85L, 1L,
# 2026L, "male", "white", 2L, 2L, 2L, 3L, 3L, 70.94328, 70.94328, 84L, 84L, 0L, 0L, 86L, 0L,
# 2027L, "female", "white", 2L, 2L, 3L, 3L, 3L, 62.90584, 65.56011, 73L, 77L, 2L, 0L, 85L, 1L,
# 2028L, "male", "white", 2L, 1L, 1L, 2L, 1L, 68.48849, 58.68647, 81L, 66L, 0L, 0L, 70L, 16L,
# 2029L, "female", "afr-amer", 2L, 1L, 0L, 0L, 2L, 51.05624, 41.31353, 52L, 34L, 0L, 0L, 79L, 6L,
# 2030L, "female", "white", 2L, 1L, 2L, 3L, 3L, 64.20476, 67.72454, 75L, 80L, 0L, 0L, 70L, 16L,
# 2031L, "male", "asian", 2L, 2L, 3L, 4L, 3L, 58.11485, 78.2363, 65L, 91L, 1L, 0L, 86L, 0L,
# 2032L, "female", "afr-amer", 2L, 0L, 2L, 2L, 3L, 46.82059, 42.45086, 44L, 36L, 0L, 0L, 77L, 8L,
# 2033L, "male", "white", 2L, 0L, 1L, 3L, 2L, 46.82059, 52.64643, 44L, 55L, 0L, 0L, 85L, 1L,
# 2034L, "female", "white", 2L, 3L, 3L, 4L, 4L, 66.98323, 86.86945, 79L, 96L, 0L, 0L, 84L, 2L,
# 2035L, "female", "white", 2L, 0L, 0L, 3L, 2L, 32.27546, 51.05624, 20L, 52L, 1L, 0L, 83L, 3L,
# 2036L, "female", "hispanic", 2L, 1L, 2L, 2L, 3L, 29.05672, 29.05672, 16L, 16L, 3L, 3L, 82L, 4L,
# 2037L, "female", "hispanic", 2L, 1L, 3L, 2L, 2L, 98.99289, 42.45086, 99L, 36L, 3L, 2L, 84L, 2L,
# 2038L, "female", "afr-amer", 2L, 3L, 2L, 4L, 2L, 61.65428, 84.64062, 71L, 95L, 0L, 0L, 82L, 4L,
# 2039L, "male", "white", 2L, 2L, 4L, 2L, 2L, 47.88486, 37.09416, 46L, 27L, 2L, 2L, 79L, 7L,
# 2040L, "female", "hispanic", 2L, 2L, 3L, 2L, 2L, 53.71444, 56.98883, 57L, 63L, 1L, 0L, 86L, 0L,
# 2041L, "female", "hispanic", 2L, 2L, 4L, 2L, 3L, 59.26457, 51.58518, 67L, 53L, 2L, 3L, 85L, 1L,
# 2042L, "female", "white", 2L, 4L, 2L, 4L, 4L, 73.72179, 93.25195, 87L, 98L, 0L, 0L, 85L, 1L,
# 2043L, "female", "white", 2L, 2L, 2L, 2L, 3L, 61.04388, 51.58518, 70L, 53L, 0L, 0L, 86L, 0L,
# 2044L, "female", "white", 2L, 0L, 1L, 1L, 1L, 33.01677, 45.2079, 21L, 41L, 0L, 0L, 73L, 13L,
# 2045L, "female", "white", 2L, 0L, 3L, 1L, 2L, 39.55739, 41.31353, 31L, 34L, 0L, 0L, 85L, 1L,
# 2046L, "male", "white", 2L, 3L, 2L, 4L, 2L, 56.98883, 62.27464, 63L, 72L, 2L, 0L, 86L, 0L,
# 2047L, "female", "hispanic", 2L, 2L, 4L, 3L, 3L, 46.82059, 47.88486, 44L, 46L, 2L, 2L, 85L, 1L,
# 2048L, "male", "white", 2L, 2L, 2L, 3L, 2L, 41.31353, 44.66451, 34L, 40L, 3L, 0L, 86L, 0L,
# 2049L, "female", "afr-amer", 2L, 2L, 3L, 3L, 4L, 65.56011, 71.82729, 77L, 85L, 0L, 0L, 85L, 1L,
# 2050L, "female", "white", 2L, 1L, 2L, 3L, 3L, 82.74353, 98.99289, 94L, 99L, 1L, 0L, 86L, 0L,
# 2051L, "female", "afr-amer", 2L, 0L, 2L, 3L, 3L, 45.2079, 44.11754, 41L, 39L, 0L, 0L, 85L, 1L,
# 2052L, "female", "white", 2L, 2L, 3L, 3L, 4L, 59.26457, 61.04388, 67L, 70L, 1L, 0L, 86L, 0L,
# 2053L, "female", "white", 2L, 1L, 2L, 2L, 2L, 55.88246, 56.98883, 61L, 63L, 1L, 0L, 84L, 2L,
# 2054L, "male", "white", 2L, 4L, 3L, 4L, 2L, 69.27759, 79.59081, 82L, 92L, 0L, 0L, 86L, 0L,
# 2055L, "female", "afr-amer", 2L, 3L, 3L, 3L, 2L, 56.98883, 59.26457, 63L, 67L, 0L, 0L, 85L, 1L,
# 2056L, "male", "white", 2L, 3L, 4L, 3L, 2L, 56.98883, 47.35357, 63L, 45L, 3L, 1L, 86L, 0L,
# 2057L, "female", "white", 2L, 3L, 4L, 4L, 3L, 65.56011, 62.27464, 77L, 72L, 1L, 0L, 82L, 4L,
# 2058L, "male", "white", 2L, 1L, 2L, 3L, 2L, 47.88486, 51.05624, 46L, 52L, 0L, 0L, 83L, 3L,
# 2059L, "male", "white", 2L, 1L, 2L, 2L, 2L, 20.40919, 40.15026, 8L, 32L, 1L, 0L, 85L, 1L,
# 2060L, "female", "hispanic", 2L, 3L, 4L, 3L, 4L, 55.88246, 81.08016, 61L, 93L, 1L, 0L, 86L, 0L,
# 2061L, "female", "asian", 2L, 3L, 1L, 2L, 3L, 61.65428, 60.44261, 71L, 69L, 0L, 0L, 85L, 1L,
# 2062L, "female", "white", 2L, 3L, 4L, 4L, 4L, 58.11485, 68.48849, 65L, 81L, 0L, 0L, 82L, 4L,
# 2063L, "female", "hispanic", 2L, 1L, 4L, 2L, 3L, 45.2079, 47.35357, 41L, 45L, 1L, 0L, 85L, 1L,
# 2064L, "male", "hispanic", 2L, 0L, 0L, 0L, 0L, 29.05672, 32.27546, 16L, 20L, 2L, 2L, 77L, 9L,
# 2065L, "female", "white", 2L, 2L, 2L, 3L, 3L, 33.73761, 59.84974, 22L, 68L, 0L, 0L, 86L, 0L,
# 2066L, "male", "hispanic", 2L, 1L, 1L, 1L, 2L, 53.71444, 40.15026, 57L, 32L, 2L, 2L, 82L, 4L,
# 2067L, "female", "asian", 2L, 3L, 2L, 3L, 1L, 50.52795, 53.71444, 51L, 57L, 2L, 0L, 54L, 8L,
# 2068L, "male", "hispanic", 2L, 0L, 2L, 1L, 0L, 63.54885, 54.25188, 74L, 58L, 0L, 1L, 73L, 13L,
# 2069L, "male", "white", 2L, 1L, 4L, 2L, 3L, 45.2079, 48.94376, 41L, 48L, 2L, 0L, 86L, 0L,
# 2070L, "male", "white", 2L, 2L, 2L, 1L, 4L, 73.72179, 56.43343, 87L, 62L, 2L, 0L, 86L, 0L,
# 2071L, "male", "white", 2L, 3L, 4L, 4L, 4L, 59.26457, 49.47205, 67L, 49L, 0L, 0L, 86L, 0L,
# 2072L, "female", "asian", 2L, 4L, 4L, 3L, 2L, 98.99289, 69.27759, 99L, 82L, 2L, 0L, 86L, 0L,
# 2073L, "female", "hispanic", 2L, 0L, 3L, 3L, 4L, 56.98883, 74.74522, 63L, 88L, 1L, 0L, 84L, 2L,
# 2074L, "female", "white", 2L, 2L, 4L, 3L, 3L, 58.11485, 58.11485, 65L, 65L, 0L, 0L, 81L, 5L,
# 2075L, "female", "white", 2L, 4L, 1L, 4L, 2L, 61.65428, 86.86945, 71L, 96L, 0L, 0L, 85L, 1L,
# 2076L, "male", "white", 2L, 2L, 2L, 4L, 2L, 65.56011, 66.98323, 77L, 79L, 1L, 0L, 86L, 0L,
# 2077L, "female", "afr-amer", 2L, 1L, 3L, 1L, 2L, 59.26457, 56.98883, 67L, 63L, 0L, 0L, 86L, 0L,
# 2078L, "female", "hispanic", 2L, 3L, 4L, 4L, 2L, 66.98323, 63.54885, 79L, 74L, 2L, 0L, 85L, 1L,
# 2079L, "female", "white", 2L, 1L, 3L, 3L, 1L, 32.27546, 50, 20L, 50L, 2L, 0L, 84L, 2L,
# 2080L, "male", "afr-amer", 2L, 3L, 4L, 3L, 3L, 70.94328, 73.72179, 84L, 87L, 0L, 0L, 84L, 1L,
# 2081L, "male", "asian", 2L, 0L, 3L, 4L, 1L, 37.72536, 37.72536, 28L, 28L, 2L, 0L, 81L, 5L,
# 2082L, "female", "white", 2L, 0L, 2L, 1L, 3L, 32.27546, 29.90528, 20L, 17L, 2L, 0L, 83L, 3L,
# 2083L, "male", "white", 2L, 0L, 0L, 2L, 3L, 36.45115, 32.27546, 26L, 20L, 1L, 0L, 85L, 1L,
# 2084L, "female", "asian", 2L, 1L, 3L, 2L, 4L, 64.20476, 71.82729, 75L, 85L, 0L, 0L, 83L, 3L,
# 2085L, "female", "white", 2L, 1L, 4L, 1L, 3L, 56.98883, 71.82729, 63L, 85L, 0L, 0L, 80L, 6L,
# 2086L, "male", "white", 2L, 0L, 4L, 2L, 1L, 44.11754, 24.16932, 39L, 11L, 1L, 0L, 78L, 8L,
# 2087L, "male", "asian", 2L, 0L, 2L, 0L, 3L, 40.15026, 40.15026, 32L, 32L, 1L, 2L, 65L, 21L,
# 2088L, "male", "hispanic", 2L, 0L, 1L, 0L, 1L, 28.17271, 30.72241, 15L, 18L, 1L, 0L, 19L, 1L,
# 2089L, "female", "white", 2L, 2L, 2L, 3L, 2L, 52.64643, 79.59081, 55L, 92L, 0L, 0L, 79L, 7L,
# 2090L, "female", "asian", 2L, 0L, 2L, 3L, 2L, 40.15026, 44.66451, 32L, 40L, 0L, 0L, 81L, 5L,
# 2091L, "male", "asian", 2L, 1L, 4L, 2L, 2L, 41.31353, 40.15026, 34L, 32L, 2L, 4L, 85L, 1L,
# 2092L, "female", "white", 2L, 0L, 2L, 3L, 2L, 59.26457, 89.60951, 67L, 97L, 0L, 0L, 85L, 1L,
# 2093L, "female", "white", 2L, 4L, 4L, 4L, 3L, 45.2079, 46.82059, 41L, 44L, 2L, 0L, 86L, 0L,
# 2094L, "male", "white", 2L, 0L, 2L, 1L, 2L, 45.2079, 53.17941, 41L, 56L, 2L, 0L, 82L, 4L,
# 2095L, "female", "hispanic", 2L, 1L, 4L, 2L, 3L, 38.34572, 55.33549, 29L, 60L, 0L, 0L, 86L, 0L,
# 2096L, "male", "white", 2L, 0L, 3L, 0L, 3L, 46.28556, 55.33549, 43L, 60L, 0L, 0L, 72L, 14L,
# 2097L, "female", "hispanic", 2L, 2L, 2L, 2L, 2L, 65.56011, 51.05624, 77L, 52L, 2L, 3L, 44L, 2L,
# 2098L, "female", "white", 2L, 1L, 3L, 2L, 3L, 51.58518, 65.56011, 53L, 77L, 2L, 0L, 84L, 2L,
# 2099L, "female", "white", 2L, 2L, 4L, 3L, 4L, 46.82059, 68.48849, 44L, 81L, 2L, 0L, 84L, 2L,
# 2100L, "male", "white", 2L, 3L, 3L, 2L, 4L, 50.52795, 43.01117, 51L, 37L, 0L, 0L, 86L, 0L,
# 2101L, "male", "white", 2L, 2L, 3L, 3L, 3L, 59.26457, 55.33549, 67L, 60L, 1L, 1L, 85L, 1L,
# 2102L, "male", "white", 2L, 0L, 2L, 0L, 0L, 49.47205, 43.01117, 49L, 37L, 0L, 0L, 67L, 19L,
# 2103L, "female", "asian", 2L, 1L, 2L, 3L, 2L, 43.01117, 46.82059, 37L, 44L, 0L, 0L, 84L, 2L,
# 2104L, "male", "white", 2L, 1L, 2L, 3L, 3L, 58.11485, 71.82729, 65L, 85L, 0L, 0L, 74L, 11L,
# 2105L, "male", "afr-amer", 2L, 2L, 2L, 3L, 3L, 46.28556, 70.94328, 43L, 84L, 0L, 0L, 86L, 0L,
# 2106L, "female", "hispanic", 2L, 3L, 2L, 3L, 3L, 48.94376, 53.71444, 48L, 57L, 2L, 2L, 81L, 5L,
# 2107L, "female", "afr-amer", 2L, 3L, 3L, 3L, 2L, 98.99289, 56.98883, 99L, 63L, 0L, 0L, 72L, 13L,
# 2108L, "female", "white", 2L, 0L, 2L, 2L, 3L, 41.31353, 50.52795, 34L, 51L, 1L, 0L, 86L, 0L,
# 2109L, "male", "white", 2L, 3L, 4L, 3L, 2L, 73.72179, 82.74353, 87L, 94L, 1L, 0L, 81L, 5L,
# 2110L, "male", "white", 2L, 2L, 1L, 1L, 3L, 64.20476, 65.56011, 75L, 77L, 0L, 0L, 83L, 3L,
# 2111L, "female", "hispanic", 2L, 0L, 1L, 1L, 1L, 53.71444, 51.58518, 57L, 53L, 2L, 2L, 84L, 2L,
# 2112L, "male", "white", 2L, 3L, 2L, 3L, 3L, 55.88246, 98.99289, 61L, 99L, 0L, 0L, 84L, 2L,
# 2113L, "male", "afr-amer", 2L, 0L, 2L, 3L, 1L, 62.90584, 56.98883, 73L, 63L, 0L, 0L, 81L, 5L,
# 2114L, "female", "white", 2L, 3L, 4L, 4L, 4L, 61.04388, 71.82729, 70L, 85L, 1L, 0L, 86L, 0L,
# 2115L, "female", "white", 2L, 4L, 4L, 3L, 4L, 98.99289, 98.99289, 99L, 99L, 0L, 0L, 83L, 3L,
# 2116L, "male", "white", 2L, 2L, 3L, 3L, 2L, 62.90584, 54.7921, 73L, 59L, 2L, 0L, 86L, 0L,
# 2117L, "male", "white", 2L, 2L, 3L, 1L, 2L, 58.68647, 60.44261, 66L, 69L, 0L, 0L, 85L, 1L,
# 2118L, "male", "hispanic", 2L, 2L, 1L, 1L, 0L, 53.71444, 35.12527, 57L, 24L, 3L, 1L, 77L, 9L,
# 2119L, "male", "white", 2L, 3L, 2L, 2L, 1L, 65.56011, 44.11754, 77L, 39L, 0L, 0L, 85L, 1L,
# 2120L, "male", "white", 2L, 1L, 3L, 1L, 3L, 51.58518, 40.15026, 53L, 32L, 3L, 0L, 86L, 0L,
# 2121L, "male", "white", 2L, 0L, 2L, 2L, 3L, 62.90584, 62.27464, 73L, 72L, 0L, 0L, 86L, 0L,
# 2122L, "male", "white", 2L, 3L, 3L, 2L, 2L, 70.94328, 58.11485, 84L, 65L, 1L, 0L, 85L, 1L,
# 2123L, "male", "hispanic", 2L, 0L, 1L, 2L, 0L, 70.09472, 48.41482, 83L, 47L, 0L, 0L, 73L, 12L,
# 2124L, "female", "white", 2L, 1L, 2L, 3L, 3L, 65.56011, 62.27464, 77L, 72L, 0L, 0L, 83L, 3L,
# 2125L, "male", "white", 2L, 2L, 2L, 3L, 3L, 46.82059, 65.56011, 44L, 77L, 2L, 2L, 86L, 0L,
# 2126L, "female", "white", 2L, 3L, 1L, 2L, 2L, 66.98323, 51.58518, 79L, 53L, 0L, 0L, 85L, 1L,
# 2127L, "male", "afr-amer", 2L, 2L, 3L, 3L, 4L, 51.58518, 59.26457, 53L, 67L, 0L, 0L, 81L, 5L,
# 2128L, "female", "white", 2L, 1L, 3L, 3L, 2L, 46.28556, 64.20476, 43L, 75L, 1L, 0L, 85L, 1L,
# 2129L, "male", "white", 2L, 1L, 4L, 3L, 2L, 47.88486, 58.68647, 46L, 66L, 0L, 0L, 85L, 1L,
# 2130L, "female", "hispanic", 2L, 1L, 3L, 3L, 3L, 41.88515, 58.11485, 35L, 65L, 2L, 1L, 78L, 7L,
# 2131L, "female", "white", 2L, 1L, 3L, 4L, 3L, 56.98883, 59.84974, 63L, 68L, 0L, 0L, 80L, 6L,
# 2132L, "female", "white", 2L, 2L, 4L, 2L, 3L, 64.20476, 81.08016, 75L, 93L, 2L, 2L, 86L, 0L,
# 2133L, "female", "white", 2L, 1L, 1L, 2L, 2L, 70.94328, 58.68647, 84L, 66L, 2L, 0L, 78L, 8L,
# 2134L, "male", "hispanic", 2L, 1L, 3L, 0L, 2L, 45.2079, 57.54914, 41L, 64L, 2L, 4L, 86L, 0L,
# 2135L, "female", "white", 2L, 1L, 3L, 2L, 1L, 40.15026, 48.41482, 32L, 47L, 2L, 0L, 84L, 1L,
# 2136L, "male", "hispanic", 2L, 1L, 2L, 2L, 2L, 25.25478, 13.13055, 12L, 4L, 3L, 2L, 86L, 0L,
# 2137L, "male", "white", 2L, 3L, 3L, 3L, 3L, 55.88246, 86.86945, 61L, 96L, 0L, 0L, 82L, 4L,
# 2138L, "female", "asian", 2L, 0L, 1L, 0L, 0L, 98.99289, 93.25195, 99L, 98L, 1L, 0L, 63L, 17L,
# 2139L, "male", "nat-amer", 2L, 2L, 2L, 1L, 2L, 59.26457, 44.11754, 67L, 39L, 0L, 0L, 80L, 6L,
# 2140L, "female", "white", 2L, 1L, 4L, 2L, 3L, 41.88515, 41.31353, 35L, 34L, 1L, 0L, 86L, 0L,
# 2141L, "female", "white", 2L, 4L, 4L, 4L, 4L, 61.04388, 56.98883, 70L, 63L, 2L, 0L, 86L, 0L,
# 2142L, "female", "white", 2L, 2L, 2L, 3L, 2L, 73.72179, 70.94328, 87L, 84L, 0L, 0L, 85L, 1L,
# 2143L, "male", "white", 2L, 3L, 4L, 3L, 2L, 61.04388, 47.88486, 70L, 46L, 2L, 0L, 83L, 3L,
# 2144L, "male", "hispanic", 2L, 0L, 2L, 3L, 2L, 53.71444, 61.04388, 57L, 70L, 1L, 0L, 84L, 1L,
# 2145L, "male", "white", 2L, 2L, 3L, 4L, 3L, 46.82059, 59.26457, 44L, 67L, 1L, 0L, 84L, 2L,
# 2146L, "female", "white", 2L, 1L, 2L, 2L, 1L, 36.45115, 46.82059, 26L, 44L, 3L, 0L, 84L, 2L,
# 2147L, "male", "white", 2L, 0L, 2L, 2L, 3L, 56.98883, 61.04388, 63L, 70L, 0L, 0L, 84L, 2L,
# 2148L, "female", "hispanic", 2L, 0L, 1L, 2L, 0L, 20.40919, 15.35938, 8L, 5L, 2L, 4L, 81L, 5L,
# 2149L, "female", "hispanic", 2L, 0L, 3L, 0L, 3L, 47.88486, 54.7921, 46L, 59L, 1L, 0L, 45L, 41L,
# 2150L, "male", "white", 2L, 2L, 4L, 2L, 2L, 56.98883, 43.01117, 63L, 37L, 2L, 2L, 83L, 3L,
# 2151L, "female", "filipino", 2L, 0L, 2L, 2L, 0L, 54.7921, 71.82729, 59L, 85L, 1L, 0L, 79L, 7L,
# 2152L, "female", "white", 2L, 3L, 3L, 2L, 3L, 47.88486, 69.27759, 46L, 82L, 0L, 0L, 85L, 1L,
# 2153L, "male", "hispanic", 2L, 1L, 2L, 0L, 2L, 36.45115, 47.88486, 26L, 46L, 2L, 0L, 85L, 1L,
# 2154L, "female", "white", 2L, 2L, 3L, 3L, 2L, 66.98323, 68.48849, 79L, 81L, 2L, 0L, 83L, 3L,
# 2155L, "female", "hispanic", 2L, 2L, 3L, 2L, 4L, 54.7921, 53.17941, 59L, 56L, 0L, 0L, 86L, 0L,
# 2156L, "female", "white", 2L, 3L, 3L, 4L, 3L, 76.98948, 69.27759, 90L, 82L, 0L, 0L, 86L, 0L,
# 2157L, "female", "white", 2L, 2L, 2L, 4L, 3L, 65.56011, 70.94328, 77L, 84L, 0L, 0L, 84L, 2L
# )
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