R: Compute profiled-likelihood (or posterior) confidence...

PLCI.mirt {mirt}

R Documentation

Compute profiled-likelihood (or posterior) confidence intervals

Description

Computes profiled-likelihood based confidence intervals. Supports the inclusion of equality constraints. Object returns the confidence intervals and whether the respective interval could be found.

Usage

PLCI.mirt(
  mod,
  parnum = NULL,
  alpha = 0.05,
  search_bound = TRUE,
  step = 0.5,
  lower = TRUE,
  upper = TRUE,
  inf2val = 30,
  NealeMiller = FALSE,
  verbose = TRUE,
  ...
)

Arguments

`mod`	a converged mirt model
`parnum`	a numeric vector indicating which parameters to estimate. Use `mod2values` to determine parameter numbers. If `NULL`, all possible parameters are used
`alpha`	two-tailed alpha critical level
`search_bound`	logical; use a fixed grid of values around the ML estimate to determine more suitable optimization bounds? Using this has much better behaviour than setting fixed upper/lower bound values and searching from more extreme ends
`step`	magnitude of steps used when `search_bound` is `TRUE`. Smaller values create more points to search a suitable bound for (up to the lower bound value visible with `mod2values`). When upper/lower bounds are detected this value will be adjusted accordingly
`lower`	logical; search for the lower CI?
`upper`	logical; search for the upper CI?
`inf2val`	a numeric used to change parameter bounds which are infinity to a finite number. Decreasing this too much may not allow a suitable bound to be located. Default is 30
`NealeMiller`	logical; use the Neale and Miller 1997 approximation? Default is `FALSE`
`verbose`	logical; include additional information in the console?
`...`	additional arguments to pass to the estimation functions

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

References

Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. doi:10.18637/jss.v048.i06

Chalmers, R. P., Pek, J., & Liu, Y. (2017). Profile-likelihood Confidence Intervals in Item Response Theory Models. Multivariate Behavioral Research, 52, 533-550. doi:10.1080/00273171.2017.1329082

Neale, M. C. & Miller, M. B. (1997). The use of likelihood-based confidence intervals in genetic models. Behavior Genetics, 27, 113-120.

Examples

## No test: 
if(interactive()) mirtCluster() #use all available cores to estimate CI's in parallel
dat <- expand.table(LSAT7)
mod <- mirt(dat, 1)

result <- PLCI.mirt(mod)
result

##      Item class parnam parnum     value lower_2.5 upper_97.5 lower_conv
## 1  Item.1  dich     a1      1 0.9879254 0.6705382  1.3819761       TRUE
## 2  Item.1  dich      d      2 1.8560605 1.6203325  2.1474211       TRUE
## 3  Item.2  dich     a1      5 1.0808847 0.7816287  1.4614714       TRUE
## 4  Item.2  dich      d      6 0.8079786 0.6373152  0.9994390       TRUE
## 5  Item.3  dich     a1      9 1.7058006 1.1965700  2.6063138       TRUE
## 6  Item.3  dich      d     10 1.8042187 1.4754050  2.3765517       TRUE
## 7  Item.4  dich     a1     13 0.7651853 0.5211915  1.0554405       TRUE
## 8  Item.4  dich      d     14 0.4859966 0.3417041  0.6365806       TRUE
## 9  Item.5  dich     a1     17 0.7357980 0.4551545  1.0555079       TRUE
## 10 Item.5  dich      d     18 1.8545127 1.6438380  2.0976038       TRUE
##    upper_conv
## 1        TRUE
## 2        TRUE
## 3        TRUE
## 4        TRUE
## 5        TRUE
## 6        TRUE
## 7        TRUE
## 8        TRUE
## 9        TRUE
## 10       TRUE

# model with constraints
mod <- mirt(dat, 'F = 1-5
                  CONSTRAIN = (1-5, a1)')

result <- PLCI.mirt(mod)
result

##     Item class parnam parnum     value lower_2.5 upper_97.5 lower_conv
## 1 Item.1  dich     a1      1 1.0111403 0.8863986  1.1416331       TRUE
## 2 Item.1  dich      d      2 1.8681305 1.6751813  2.0690619       TRUE
## 3 Item.2  dich      d      6 0.7909392 0.6334650  0.9518291       TRUE
## 4 Item.3  dich      d     10 1.4608781 1.2848562  1.6429949       TRUE
## 5 Item.4  dich      d     14 0.5214695 0.3681968  0.6770358       TRUE
## 6 Item.5  dich      d     18 1.9928267 1.7937789  2.2005130       TRUE
##   upper_conv
## 1       TRUE
## 2       TRUE
## 3       TRUE
## 4       TRUE
## 5       TRUE
## 6       TRUE

mod2 <- mirt(Science, 1)
result2 <- PLCI.mirt(mod2)
result2

##       Item  class parnam parnum      value  lower_2.5 upper_97.5 lower_conv
## 1  Comfort graded     a1      1  1.0417547  0.7008509   1.453043       TRUE
## 2  Comfort graded     d1      2  4.8641542  4.0112194   5.966782       TRUE
## 3  Comfort graded     d2      3  2.6399417  2.2332766   3.115799       TRUE
## 4  Comfort graded     d3      4 -1.4660135 -1.7996417  -1.171326       TRUE
## 5     Work graded     a1      5  1.2259618  0.8942261   1.620993       TRUE
## 6     Work graded     d1      6  2.9240027  2.4851419   3.430756       TRUE
## 7     Work graded     d2      7  0.9011651  0.6307977   1.195238       TRUE
## 8     Work graded     d3      8 -2.2665647 -2.6975967  -1.893557       TRUE
## 9   Future graded     a1      9  2.2933717  1.5687257   3.986967       TRUE
## 10  Future graded     d1     10  5.2339928  4.1279881   7.822343       TRUE
## 11  Future graded     d2     11  2.2137728  1.6589420   3.416513       TRUE
## 12  Future graded     d3     12 -1.9637062 -3.0256934  -1.453916       TRUE
## 13 Benefit graded     a1     13  1.0949151  0.7659052   1.501997       TRUE
## 14 Benefit graded     d1     14  3.3479196  2.8453841   3.940600       TRUE
## 15 Benefit graded     d2     15  0.9916289  0.7267311   1.282508       TRUE
## 16 Benefit graded     d3     16 -1.6882599 -2.0443917  -1.375841       TRUE
##    upper_conv
## 1        TRUE
## 2        TRUE
## 3        TRUE
## 4        TRUE
## 5        TRUE
## 6        TRUE
## 7        TRUE
## 8        TRUE
## 9        TRUE
## 10       TRUE
## 11       TRUE
## 12       TRUE
## 13       TRUE
## 14       TRUE
## 15       TRUE
## 16       TRUE

# only estimate CI's slopes
sv <- mod2values(mod2)
parnum <- sv$parnum[sv$name == 'a1']
result3 <- PLCI.mirt(mod2, parnum)
result3

##      Item  class parnam parnum    value lower_2.5 upper_97.5 lower_conv
## 1 Comfort graded     a1      1 1.041755 0.7008509   1.453043       TRUE
## 2    Work graded     a1      5 1.225962 0.8942261   1.620993       TRUE
## 3  Future graded     a1      9 2.293372 1.5687257   3.986967       TRUE
## 4 Benefit graded     a1     13 1.094915 0.7659052   1.501997       TRUE
##   upper_conv
## 1       TRUE
## 2       TRUE
## 3       TRUE
## 4       TRUE

## End(No test)

[Package mirt version 1.40 Index]