lrv2ord | R Documentation |

This function calculates ordinal-scale moments implied by LRV-scale moments

lrv2ord(Sigma, Mu, thresholds, cWts)

`Sigma` |
Population covariance |

`Mu` |
Optional |

`thresholds` |
Either a single |

`cWts` |
Optional (default when missing is to use 0 for the lowest
category, followed by successive integers for each higher category).
Either a single |

Binary and ordinal data are frequently accommodated in SEM by incorporating a threshold model that links each observed categorical response variable to a corresponding latent response variable that is typically assumed to be normally distributed (Kamata & Bauer, 2008; Wirth & Edwards, 2007).

A `list`

including the LRV-scale population moments (means,
covariance matrix, correlation matrix, and thresholds), the category
weights, a `data.frame`

of implied univariate moments (means,
*SD*s, skewness, and excess kurtosis (i.e., in excess of 3, which is
the kurtosis of the normal distribution) for discretized data treated as
`numeric`

, and the implied covariance and correlation matrix of
discretized data treated as `numeric`

.

Terrence D. Jorgensen (University of Amsterdam; TJorgensen314@gmail.com)

Andrew Johnson (Curtin University; andrew.johnson@curtin.edu.au)

Kamata, A., & Bauer, D. J. (2008). A note on the relation between factor
analytic and item response theory models.
*Structural Equation Modeling, 15*(1), 136–153.
doi: 10.1080/10705510701758406

Wirth, R. J., & Edwards, M. C. (2007). Item factor analysis: Current
approaches and future directions. *Psychological Methods, 12*(1),
58–79. doi: 10.1037/1082-989X.12.1.58

## SCENARIO 1: DIRECTLY SPECIFY POPULATION PARAMETERS ## specify population model in LISREL matrices Nu <- rep(0, 4) Alpha <- c(1, -0.5) Lambda <- matrix(c(1, 1, 0, 0, 0, 0, 1, 1), nrow = 4, ncol = 2, dimnames = list(paste0("y", 1:4), paste0("eta", 1:2))) Psi <- diag(c(1, .75)) Theta <- diag(4) Beta <- matrix(c(0, .5, 0, 0), nrow = 2, ncol = 2) ## calculate model-implied population means and covariance matrix ## of latent response variables (LRVs) IB <- solve(diag(2) - Beta) # to save time and space Mu_LRV <- Nu + Lambda %*% IB %*% Alpha Sigma_LRV <- Lambda %*% IB %*% Psi %*% t(IB) %*% t(Lambda) + Theta ## Specify (unstandardized) thresholds to discretize normally distributed data ## generated from Mu_LRV and Sigma_LRV, based on marginal probabilities PiList <- list(y1 = c(.25, .5, .25), y2 = c(.17, .33, .33, .17), y3 = c(.1, .2, .4, .2, .1), ## make final variable highly asymmetric y4 = c(.33, .25, .17, .12, .08, .05)) sapply(PiList, sum) # all sum to 100% CumProbs <- sapply(PiList, cumsum) ## unstandardized thresholds TauList <- mapply(qnorm, p = lapply(CumProbs, function(x) x[-length(x)]), m = Mu_LRV, sd = sqrt(diag(Sigma_LRV))) for (i in 1:4) names(TauList[[i]]) <- paste0(names(TauList)[i], "|t", 1:length(TauList[[i]])) ## assign numeric weights to each category (optional, see default) NumCodes <- list(y1 = c(-0.5, 0, 0.5), y2 = 0:3, y3 = 1:5, y4 = 1:6) ## Calculate Population Moments for Numerically Coded Ordinal Variables lrv2ord(Sigma = Sigma_LRV, Mu = Mu_LRV, thresholds = TauList, cWts = NumCodes) ## SCENARIO 2: USE ESTIMATED PARAMETERS AS POPULATION data(datCat) # already stored as c("ordered","factor") fit <- cfa(' f =~ 1*u1 + 1*u2 + 1*u3 + 1*u4 ', data = datCat) lrv2ord(Sigma = fit, thresholds = fit) # use same fit for both ## or use estimated thresholds with specified parameters, but note that ## lrv2ord() will only extract standardized thresholds dimnames(Sigma_LRV) <- list(paste0("u", 1:4), paste0("u", 1:4)) lrv2ord(Sigma = cov2cor(Sigma_LRV), thresholds = fit)

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.