slm {pks} | R Documentation |
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,
checkK = TRUE)
getSlmPK(g, K, Ko)
## 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 space. 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 |
|
R |
a person-by-problem indicator matrix of unique response patterns.
Per default inferred from the names of |
beta , eta , g |
vectors of initial values for the error, guessing, and solvability parameters. |
betafix , etafix |
vectors of fixed error and guessing parameter values;
|
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 |
incradius |
include knowledge states of distance from the minimum
discrepant states less than or equal to |
tol |
tolerance, stopping criterion for iteration. |
maxiter |
the maximum number of iterations. |
zeropad |
the maximum number of items for which an incomplete
|
checkK |
logical, if |
Ko |
a state-by-problem indicator matrix representing the outer fringe
for each knowledge state in |
x |
an object of class |
P.Kshow |
logical, should the estimated distribution of knowledge states be printed? |
parshow |
logical, should the estimates of error, guessing, and solvability parameters be printed? |
digits |
a non-null value for |
... |
additional arguments passed to other methods. |
Details
See Doignon and Falmagne (1999) for details on the simple learning model
(SLM) for probabilistic knowledge structures. The model requires a
well-graded knowledge space K
.
An slm
object inherits from class blim
. See blim
for
details on the function arguments. The helper function getSlmPK
returns the distribution of knowledge states P.K
.
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 solvability parameters. |
References
Doignon, J.-P., & Falmagne, J.-C. (1999). Knowledge spaces. Berlin: Springer.
See Also
blim
, simulate.blim
, getKFringe
,
is.downgradable
Examples
data(DoignonFalmagne7)
K <- DoignonFalmagne7$K # well-graded knowledge space
N.R <- DoignonFalmagne7$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)