predict.blim: Predict Knowledge States from Basic Local Independence Models (BLIMs)

Description

Predict knowledge state or state probabilities based on a fitted blim object given a response pattern.

Usage

# S3 method for blim
predict(object, newdata = NULL, type = c("state", "probs"),
        method = c("ML", "MD", "MDML"), quiet = FALSE,
        ties.method = c("min", "max", "random"), i.RK = NULL,
        incradius = object$incradius, as.pattern = TRUE, ...)

Value

If type = "state", a character vector of knowledge states (if

as.pattern = TRUE) or a state-by-problem indicator matrix (if

as.pattern = FALSE).

If type = "probs", a matrix of posterior state probabilities.

Arguments

object: an object of class blim, typically the result of a call to blim.
newdata: a character vector of response patterns with which to predict.
type: for each pattern, predict a knowledge state or the state probabilities.
method: how to compute the posterior state probabilities. (See Details.)
quiet: silence message when estimation and prediction methods differ.
ties.method: how to deal with a posteriori equally probable states.
i.RK: optional indicator matrix of states at minimum distance from response patterns.
incradius: see blim.
as.pattern: return a character vector via as.pattern or an indicator matrix.
...: further arguments passed to as.pattern.

Details

Predicted is the modal posterior state (type = "state") or the posterior distribution (type = "probs") of knowledge states given a response pattern. Depending on the method argument, the posterior distribution is defined as:

Maximum likelihood (method = "ML") $$P(K | R)_{ML} = \frac{P(R | K) P(K)}{\sum_K P(R | K) P(K)} = \frac{P(R | K) P(K)}{P(R)}$$
Minimum discrepancy (method = "MD") $$P(K | R)_{MD} = \frac{i_{RK}}{\sum_K i_{RK}}$$
Minimum discrepancy ML (method = "MDML") $$P(K | R)_{MDML} = \frac{i_{RK} \cdot P(K | R)_{ML}} {\sum_K i_{RK} \cdot P(K | R)_{ML}}$$

where $i_{RK}$ is a pattern-by-state indicator matrix that is one for each state $K$ that is at minimum distance from pattern $R$.

Examples

Run this code

data(DoignonFalmagne7)
m <- blim(DoignonFalmagne7$K, DoignonFalmagne7$N.R)
predict(m)
predict(m, newdata = c("00100", "10100", "01111"), as.pattern = FALSE)

m <- slm(DoignonFalmagne7$K, DoignonFalmagne7$N.R)
predict(m, newdata = "00100")

data(endm)
m <- blim(endm$K, endm$N.R)
predict(m, type = "probs", method = "MD")
cbind(
  observed = names(m$N.R),
  min = predict(m, method = "MD", ties.method = "min"),
  max = predict(m, method = "MD", ties.method = "max"),
  rnd = predict(m, method = "MD", ties.method = "random")
) |> print(quote = FALSE)