slm: Simple Learning Models (SLMs)

In pks: Probabilistic Knowledge Structures

Simple Learning Models (SLMs)

Description

Fits a simple learning model (SLM) for probabilistic knowledge structures by minimum discrepancy maximum likelihood estimation.

Usage

slm(K, N.R, method = c("MD", "ML", "MDML"), R = as.binmat(N.R),
    beta = rep(0.1, nitems), eta = rep(0.1, nitems),
    g = rep(0.1, nitems),
    betafix = rep(NA, nitems), etafix = rep(NA, nitems),
    betaequal = NULL, etaequal = NULL,
    randinit = FALSE, incradius = 0,
    tol = 1e-07, maxiter = 10000, zeropad = 16)

## S3 method for class 'slm'
print(x, P.Kshow = FALSE, parshow = TRUE,
      digits=max(3, getOption("digits") - 2), ...)

Arguments

K	a state-by-problem indicator matrix representing the knowledge structure. An element is one if the problem is contained in the state, and else zero.
N.R	a (named) vector of absolute frequencies of response patterns.
method	MD for minimum discrepancy estimation, ML for maximum likelihood estimation, MDML for minimum discrepancy maximum likelihood estimation.
R	a person-by-problem indicator matrix of unique response patterns. Per default inferred from the names of N.R.
beta, eta, g	vectors of initial values for the error, guessing, and learning parameters.
betafix, etafix	vectors of fixed error and guessing parameter values; NA indicates a free parameter.
betaequal, etaequal	lists of vectors of problem indices; each vector represents an equivalence class: it contains the indices of problems for which the error or guessing parameters are constrained to be equal. (See Examples.)
randinit	logical, if TRUE then initial parameter values are sampled uniformly with constraints. (See Details.)
incradius	include knowledge states of distance from the minimum discrepant states less than or equal to incradius.
tol	tolerance, stopping criterion for iteration.
maxiter	the maximum number of iterations.
zeropad	the maximum number of items for which an incomplete N.R vector is completed and padded with zeros.
x	an object of class slm, typically the result of a call to slm.
P.Kshow	logical, should the estimated distribution of knowledge states be printed?
parshow	logical, should the estimates of error, guessing, and learning parameters be printed?
digits	a non-null value for digits specifies the minimum number of significant digits to be printed in values.
...	additional arguments passed to other methods.

Details

See Doignon and Falmagne (1999) for details on the simple learning model (SLM) for probabilistic knowledge structures.

An slm object inherits from class blim. See blim for details on the function arguments.

Value

An object of class slm and blim. It contains all components of a blim object. In addition, it includes:

g	the vector of estimates of the learning parameters parameters.

References

Doignon, J.-P., & Falmagne, J.-C. (1999). Knowledge spaces. Berlin: Springer.

See Also

blim, simulate.blim.

Examples

data(DoignonFalmagne7)
K   <- DoignonFalmagne7$K     # knowledge structure
N.R <- DoignonFalmagne7$N.R   # frequencies of response patterns

## Fit simple learning model (SLM) by different methods
slm(K, N.R, method = "MD")    # minimum discrepancy estimation
slm(K, N.R, method = "ML")    # maximum likelihood estimation by EM
slm(K, N.R, method = "MDML")  # MDML estimation

## Compare SLM and BLIM
m1 <-  slm(K, N.R, method = "ML")
m2 <- blim(K, N.R, method = "ML")
anova(m1, m2)

pks documentation built on May 5, 2023, 3:08 p.m.