| Type: | Package |
| Title: | Higher-Order Item Response Theory |
| Version: | 1.3.1 |
| Date: | 2022-08-14 |
| Maintainer: | Michael Kleinsasser <mjkleinsa@gmail.com> |
| Description: | Higher-order latent trait theory (item response theory). We implement the generalized partial credit model with a second-order latent trait structure. Latent regression can be done on the second-order latent trait. For a pre-print of the methods, see, "Latent Regression in Higher-Order Item Response Theory with the R Package hlt" https://mkleinsa.github.io/doc/hlt_proof_draft_brmic.pdf. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Depends: | R (≥ 3.5.0) |
| Imports: | Rcpp (≥ 1.0.8), RcppDist, RcppProgress, tidyr, ggplot2, truncnorm, foreach, doParallel |
| LinkingTo: | Rcpp, RcppDist, RcppProgress |
| RoxygenNote: | 7.2.1 |
| Encoding: | UTF-8 |
| URL: | https://github.com/mkleinsa/hlt |
| BugReports: | https://github.com/mkleinsa/hlt/issues |
| LazyData: | true |
| NeedsCompilation: | yes |
| Packaged: | 2022-08-19 15:55:47 UTC; mk |
| Author: | Michael Kleinsasser [aut, cre] |
| Repository: | CRAN |
| Date/Publication: | 2022-08-22 10:30:02 UTC |
asti data
Description
asti data
References
Levenson, M. R., Jennings, P. A., Aldwin, C. M., & Shiraishi, R. W. (2005). Self-transcendence: conceptualization and measurement. The International Journal of Aging and Human Development, 60, 127-143.
hlt Starting Values
Description
Get starting values from hlt fit object
Usage
get_hlt_start(x, nchains = 1)
Arguments
x |
hlt model fit object |
nchains |
number of chains to get starting values |
Value
a list of lists with starting values for each chain
Explanatory and Descriptive Higher-Order Item Response Theory (Latent Trait Theory)
Description
Fit a higher-order item response theory model under the generalized partial credit measurement model. The goal is to explain multiple latent dimensions by a single higher-order dimension. We extend this model with an option to perform regression on the general latent dimension.
Usage
hlt(
x,
z = NULL,
id,
iter,
burn = iter/2,
delta,
type = "2p",
start = list(list(lambda = c(), theta = c(), delta = c(), alpha = c(), beta = c())),
nchains = 1,
progress = TRUE,
verbose = FALSE
)
Arguments
x |
matrix of item responses. Responses must be integers where the lowest value is 0 and the highest value is the maximum possible response for the item with no gaps. If a question is asked with 5 possible responses, then the possible values should be c(0,1,2,3,4). For binary items, use c(0,1). |
z |
centered numeric matrix of predictors for the latent regression. Default is 'z = NULL' so that no regression is performed. All columns of this matrix must be numeric. For binary items, use the values c(0,1). For continuous items, center the values on the mean and divide by the standard deviation (normalized). For factors with more than two levels, recode into multiple columns of c(0,1). |
id |
I.D. vector indexing first-order latent dimension membership for each of the first-order latent dimensions. We index starting from zero, not one. If there are three first-order . latent dimensions with 5 questions per dimension, then the vector will look like c(0,0,0,0,0,1,1,1,1,1,2,2,2,2,2). |
iter |
number of total iterations. |
burn |
number of burn in iterations. |
delta |
tuning parameter for Metropolis-Hanstings algorithm. Alter delta until acceptance.ratio =~ 0.234. |
type |
type of Partial Credit Model to fit. If the partial credit model is desired (i.e. all alpha parameters = 1), then choose 'type = "1p"'. If the Generalized Parial Credit Model is desired, then choose 'type = "2p"'. The default is 'type = "2p"'. |
start |
starting values for the Metropolis-Hastings algorithm. |
nchains |
number of independent MCMC chains. Default is 'nchains = 1'. |
progress |
boolean, show progress bar? Defaults to TRUE. |
verbose |
print verbose messages. Defaults to 'FALSE'. Provide a 'list' with the following named arguments: 'list(lambda = c(), theta = c(), delta = c(), alpha = c(), beta = c())'
If you choose specify starting values, then the lengths of the starting value vectors must match the number of parameters in the model. |
Value
A 'list' containing:
post - A 'matrix' of posterior estimates. Rows are the draws and columns are the named parameters.
accept.rate - acceptance rate of MH algorithm
theta - 'matrix' of mean (first column) and standard deviation (second column) of posterior estimates of ability parameters
nT - number of latent factors estimated
args - returns the arguments to hlt
Examples
# set seed
set.seed(153)
# load the asti data set
data("asti")
# shift responses to range from 0 instead of 1
x = as.matrix(asti[, 1:25]) - 1
# subset and transform predictor data
z = asti[, 26:27]
z[, 1] = (z[, 1] == "students") * 1
z[, 2] = (z[, 2] == "male") * 1
z = as.matrix(z)
# specify which items from x belong to each domain
id = c(0,0,0,0,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4)
# fit the model
mod = hlt(x, z = z, id = id, iter = 20, burn = 10, delta = 0.002)
mod$accept.rate # ideally 0.234
plot(mod, param = "lambda1", type = "trace")
plot(mod, param = "lambda2", type = "trace")
plot(mod, param = "lambda3", type = "trace")
plot(mod, param = "a1", type = "trace")
plot(mod, param = "d2_3", type = "trace")
plot(mod, param = "beta1", type = "trace")
plot(mod, item = 1, type = "icc")
plot(mod, item = 2, type = "icc")
plot(mod, item = 3, type = "icc")
plot(mod, item = 4, type = "icc")
plot(mod, item = 5, type = "icc")
plot(mod, item = 6, type = "icc")
plot(mod, item = 7, type = "icc", min = -10, max = 10)
summary(mod, param = "all")
summary(mod, param = "delta", digits = 2)
summary(mod, param = "lambda")
summary(mod, param = "alpha")
summary(mod, param = "delta")
summary(mod, param = "theta", dimension = 1)
summary(mod, param = "theta", dimension = 2)
summary(mod, param = "theta", dimension = 3)
summary(mod, param = "theta", dimension = 4)
# start from a previous run's solution
post = tail(mod$post, 1)
start = list(lambda = post[1, c("lambda1", "lambda2", "lambda3", "lambda4", "lambda5")],
theta = mod$theta_mean,
delta = post[1, grepl("^[d]", colnames(post))],
alpha = post[1, paste0("a", 1:25)],
beta = post[1, c("beta1", "beta2")])
mod = hlt(x, z = z, id = id, start = start, iter = 20, burn = 10, delta = 0.002)
Simulate the HLT model
Description
Simulate the HLT model
Usage
hltsim(type, n, ntheta, lambda, id, dL, nB, beta = NULL)
Arguments
type |
type of model to simulate. 'type = "1p"' for the partial credit model. 'type = "2p"' for the generalized partial credit model. |
n |
number of observations |
ntheta |
number first-level of latent dimensions |
lambda |
latent factor coefficients |
id |
number of questions |
dL |
number of levels for each question |
nB |
number of regression parameters. nB = ncol(z). |
beta |
what value to set the regression parameters. |
Value
a 'list' containing
x - matrix of simulated item responses
theta - matrix of true latent ability
id - I.Ds for item membership to each dimension
namesx - vector of column names for each item
s.cor - true correlations between latent ability dimensions
s.delta - true difficulty parameters
s.lambda - true loading parameters
s.alpha - true discrimination parameters
Examples
xdat = hltsim(n = 250, type = "2p", ntheta = 4,
lambda = c(0.5, 0.8, 0.9, 0.4), id = c(rep(0, 15),
rep(1, 15), rep(2, 15), rep(3, 15)), dL = 2)
mod1 = hlt(x = xdat$x, id = xdat$id, iter = 12e1,
burn = 6e1, delta = 0.023)
xdat = hltsim(n = 250, type = "2p", ntheta = 4,
lambda = c(0.5, 0.8, 0.9, 0.4), id = c(rep(0, 15),
rep(1, 15), rep(2, 15), rep(3, 15)), dL = 2,
beta = c(0.5, -0.7), nB = 2)
mod2 = hlt(x = xdat$x, id = xdat$id, z = xdat$z,
iter = 12e1, burn = 6e1, delta = 0.023, nchains = 1)
Merge Chains from hlt method
Description
Merge Chains from hlt method
Usage
merge_chains(x, ...)
Arguments
x |
object of class "hltObjList" |
... |
other arguments |
Value
a list of class 'hltObj'. This class constructs a single 'hltObj' from a list of model fits by merging the chains into one matrix of draws.