umxThresholdMatrix: Create the threshold matrix needed for modeling ordinal data.

Description

High-level helper for ordinal modeling. Creates, labels, and sets smart-starts for this complex matrix. Big time saver!

Usage

umxThresholdMatrix(df, sep = NA, method = c("auto", "Mehta", "allFree"),
  thresholds = c("deviationBased", "direct", "ignore", "left_censored"),
  threshMatName = "threshMat", l_u_bound = c(NA, NA), droplevels = FALSE,
  suffixes = "deprecated", verbose = FALSE)

Arguments

the data being modeled (to allow access to the factor levels and quantiles within these for each variable)

sep

(optional) string for wide (twin) data, separating the base name from a numeric suffix (e.g. "_T")

method

How to set the thresholds: auto (the default), Mehta, which fixes the first two (auto chooses this for ordinal) or "allFree" (auto chooses this for binary)

thresholds

How to implement thresholds: "deviationBased" (default), "direct", "ignore", "left_censored"

threshMatName

name of the matrix which is returned. Defaults to "threshMat" - best not to change it.

l_u_bound

c(NA, NA) by default, you can use this to bound the thresholds. Careful you don't set bounds too close if you do.

droplevels

Whether to drop levels with no observed data (defaults to FALSE)

suffixes

deprecated. Instead of c("T1", "T2"), set sep (see above)

verbose

(defaults to FALSE))

Value

- thresholds matrix

Details

When modeling ordinal data (sex, low-med-hi, depressed/normal, not at all, rarely, often, always), a useful conceptual strategy to handle expectations is to build a standard-normal model (i.e., a latent model with zero-means, and unit (1.0) variances), and then to threshold this normal distribution to generate the observed data. Thus an observation of "depressed" is modeled as a high score on the latent normally distributed trait, with thresholds set so that only scores above this threshold (1-minus the number of categories).

For deviation methods, it returns a list of lowerOnes_for_thresh, deviations_for_thresh & thresholdsAlgebra (named threshMatName)

For direct, it returns a thresholdsMatrix (named threshMatName)

References

- http://tbates.github.io, https://github.com/tbates/umx

Examples

Run this code

# NOT RUN {
x = data.frame(ordered(rbinom(100,1,.5))); names(x) <- c("x")
umxThresholdMatrix(x)
x = cut(rnorm(100), breaks = c(-Inf,.2,.5, .7, Inf)); levels(x) = 1:5
x = data.frame(ordered(x)); names(x) <- c("x")
tmp = umxThresholdMatrix(x)

# ==================
# = Binary example =
# ==================
require(umx)
if(!packageVersion("OpenMx") > 2.5){message("Update OpenMx to get a new version of twinData")}
data(twinData)
# ===============================================================
# = Create a series of binary and ordinal columns to work with =
# ===============================================================
# Cut to form category of 80 % obese subjects
selDVs = c("obese1", "obese2")
obesityLevels = c('normal', 'obese')
cutPoints <- quantile(twinData[, "bmi1"], probs = .2, na.rm = TRUE)
twinData$obese1 <- cut(twinData$bmi1, breaks = c(-Inf, cutPoints, Inf), labels = obesityLevels) 
twinData$obese2 <- cut(twinData$bmi2, breaks = c(-Inf, cutPoints, Inf), labels = obesityLevels) 
# Step 2: Make the ordinal variables into mxFactors
# this ensures ordered= TRUE + requires user to confirm levels
twinData[, selDVs] <- mxFactor(twinData[, selDVs], levels = obesityLevels)

# Repeat for three-level weight variable
selDVs = c("obeseTri1", "obeseTri2")
obesityLevels = c('normal', 'overweight', 'obese')
cutPoints <- quantile(twinData[, "bmi1"], probs = c(.4, .7), na.rm = TRUE)
twinData$obeseTri1 <- cut(twinData$bmi1, breaks = c(-Inf, cutPoints, Inf), labels = obesityLevels) 
twinData$obeseTri2 <- cut(twinData$bmi2, breaks = c(-Inf, cutPoints, Inf), labels = obesityLevels) 
twinData[, selDVs] <- mxFactor(twinData[, selDVs], levels = obesityLevels)

selDVs = c("obeseQuad1", "obeseQuad2")
obesityLevels = c('underWeight', 'normal', 'overweight', 'obese')
cutPoints <- quantile(twinData[, "bmi1"], probs = c(.25, .4, .7), na.rm = TRUE)
twinData$obeseQuad1 <- cut(twinData$bmi1, breaks = c(-Inf, cutPoints, Inf), labels = obesityLevels) 
twinData$obeseQuad2 <- cut(twinData$bmi2, breaks = c(-Inf, cutPoints, Inf), labels = obesityLevels) 
twinData[, selDVs] <- mxFactor(twinData[, selDVs], levels = obesityLevels)

# Example 1
selDVs = c("obese1", "obese2")
tmp = umxThresholdMatrix(twinData[,selDVs], sep = "", verbose = TRUE) # informative messages

# ======================================
# = Ordinal (n categories > 2) example =
# ======================================
selDVs = c("obeseTri1", "obeseTri2")
tmp = umxThresholdMatrix(twinData[,selDVs], sep = "", verbose = TRUE)

# ========================================================
# = Mix of all three kinds example (and a 4-level trait) =
# ========================================================

selDVs = umx_paste_names(c("bmi", "obese", "obeseTri", "obeseQuad"), "", 1:2)
tmp = umxThresholdMatrix(twinData[,selDVs], sep = "", verbose = TRUE)
str(tmp)

# }

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