adaptive_test: Ability parameter estimation with fixed item parameters

In IRTest: Parameter Estimation of Item Response Theory with Estimation of Latent Distribution

Ability parameter estimation with fixed item parameters

Description

Ability parameter estimation when item responses and item parameters are given. This function can be useful in ability parameter estimation is adaptive testing.

Usage

adaptive_test(
  response,
  item,
  model = "dich",
  ability_method = "EAP",
  quad = NULL,
  prior = NULL
)

Arguments

response	A matrix of item responses. For mixed-format test, a list of item responses where dichotomous item responses are the first element and polytomous item responses are the second element.
item	A matrix of item parameters. For mixed-format test, a list of item parameters where dichotomous item parameters are the first element and polytomous item parameters are the second element.
model	dich for dichotomous items, cont for continuous items, and a specific item response model (e.g., PCM, GPCM, GRM) for polytomous items and a mixed-format test. The default is dich.
ability_method	The ability parameter estimation method. The available options are Expected a posteriori (EAP), Maximum Likelihood Estimates (MLE), and weighted likelihood estimates (WLE). The default is EAP.
quad	A vector of quadrature points for EAP calculation. If NULL is passed, it is set as seq(-6,6,length.out=121). The default is NULL.
prior	A vector of the prior distribution for EAP calculation. The length of it should be the same as quad. If NULL is passed, the standard normal distribution is used. The default is NULL.

Value

theta	The estimated ability parameter values. If ability_method = "MLE". If an examinee receives a maximum or minimum score for all items, the function returns \pmInf.
theta_se	The standard errors of ability parameter estimates. It returns standard deviations of posteriors for EAPs and asymptotic standard errors (i.e., square root of inverse Fisher information) for MLE. If an examinee receives a maximum or minimum score for all items, the function returns NA for MLE.

Author(s)

Seewoo Li [e-mail]

Examples

# dichotomous

response <- c(1,1,0)
item <- matrix(
  c(
      1, -0.5,   0,
    1.5,   -1,   0,
    1.2,    0, 0.2
  ), nrow = 3, byrow = TRUE
)
adaptive_test(response, item, model = "dich", ability_method = "WLE")


# polytomous

response <- c(1,2,0)
item <- matrix(
    c(
      1, -0.5, 0.5,
    1.5,   -1,   0,
    1.2,    0, 0.4
    ), nrow = 3, byrow = TRUE
  )
adaptive_test(response, item, model="GPCM", ability_method = "WLE")


# mixed-format test

response <- list(c(0,0,0),c(2,2,1))
item <- list(
  matrix(
    c(
        1, -0.5, 0,
      1.5,   -1, 0,
      1.2,    0, 0
    ), nrow = 3, byrow = TRUE
  ),
  matrix(
    c(
        1, -0.5, 0.5,
      1.5,   -1,   0,
      1.2,    0, 0.4
    ), nrow = 3, byrow = TRUE
  )
)
adaptive_test(response, item, model = "GPCM", ability_method = "WLE")


# continuous response

response <- c(0.88, 0.68, 0.21)
item <- matrix(
  c(
    1, -0.5, 10,
    1.5,   -1,  8,
    1.2,    0, 11
  ), nrow = 3, byrow = TRUE
)
adaptive_test(response, item, model = "cont", ability_method = "WLE")

IRTest documentation built on Oct. 4, 2024, 5:11 p.m.