# lc2_agreement: A Latent Class Model for Agreement of Two Raters In immer: Item Response Models for Multiple Ratings

## Description

Estimates a latent class model for agreement of two raters (Schuster & Smith, 2006). See Details for the description of the model.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```lc2_agreement(y, w = rep(1, nrow(y)), type = "homo", method = "BFGS", ...) ## S3 method for class 'lc2_agreement' summary(object, digits=3,...) ## S3 method for class 'lc2_agreement' logLik(object, ...) ## S3 method for class 'lc2_agreement' anova(object, ...) ```

## Arguments

 `y` A data frame containing the values of two raters in columns `w` Optional vector of weights `type` Type of model specification. Can be `"unif"`, `"equal"`, `"homo"` or `"hete"`. See Details. `method` Optimization method used in `stats::optim` `...` Further arguments passed to `stats::optim` `object` Object of class `l2_agreement` `digits` Number of digits for rounding

## Details

The latent class model for two raters decomposes a portion of ratings which conform to true agreement and another portion of ratings which conform to a random rating of a category. Let X_r denote the rating of rater r, then for i \neq j, it is assumed that

P(X_1 = i , X_2 = j) = φ_{1i} φ_{2j} ( 1 - γ )

For i = j it is assumed that

P(X_1 = i , X_2 = i) = τ_i γ + φ_{1i} φ_{2i} ( 1 - γ )

where γ denotes the proportion of true ratings.

All τ_i and φ_{ri} parameters are estimated using `type="hete"`. If the φ parameters are assumed as invariant across the two raters (i.e. φ_{1i}=φ_{2i}=φ_{i}), then `type="homo"` must be specified. The constraint τ_i = φ_i is imposed by `type="equal"`. All φ_i parameters are set equal to each other using `type="unif"`.

## Value

 `model_output` Output of the fitted model `saturated_output` Output of the saturated model `LRT_output` Output of the likelihood ratio test of model fit `partable` Parameter table `parmsummary` Parameter summary `agree_true` True agreement index shich is the γ parameter `agree_chance` Agreement by chance `rel_agree` Conditional reliability of agreement `optim_output` Output of `optim` from the fitted model `nobs` Number of observations `type` Model type `ic` Information criteria `loglike` Log-likelihood `npars` Number of parameters `y` Used dataset `w` Used weights

## Author(s)

Alexander Robitzsch

## References

Schuster, C., & Smith, D. A. (2006). Estimating with a latent class model the reliability of nominal judgments upon which two raters agree. Educational and Psychological Measurement, 66(5), 739-747.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33``` ```############################################################################# # EXAMPLE 1: Dataset in Schuster & Smith (2006) ############################################################################# data(data.immer08) dat <- data.immer08 # select ratings and frequency weights y <- dat[,1:2] w <- dat[,3] #*** Model 1: Uniform distribution phi parameters mod1 <- immer::lc2_agreement( y = y , w = w , type="unif") summary(mod1) #*** Model 2: Equal phi and tau parameters mod2 <- immer::lc2_agreement( y = y , w = w , type="equal") summary(mod2) ## Not run: #*** Model 3: Homogeneous rater model mod3 <- immer::lc2_agreement( y = y , w = w , type="homo") summary(mod3) #*** Model 4: Heterogeneous rater model mod4 <- immer::lc2_agreement( y = y , w = w , type="hete") summary(mod4) #--- some model comparisons anova(mod3,mod4) IRT.compareModels(mod1,mod2,mod3,mod4) ## End(Not run) ```

immer documentation built on May 29, 2017, 10:07 p.m.