# Functionalities

The equateMultiple package computes:

• Equating coefficients between multiple forms.
• Synthetic item parameters (sort of mean of the item parameter estimates from different forms).
• Standard errors of the equating coefficients and the synthetic item parameters.

# Data preparation

Data preparation follows the same steps of the equateIRT package.

Load the package equateMultiple and the data

```library("equateMultiple")
data("data2pl", package = "equateIRT")
```

Estimate a two parameter logistic model for 5 data sets with the R package ltm

```library("ltm")
m1 <- ltm(data2pl[[1]] ~ z1)
m2 <- ltm(data2pl[[2]] ~ z1)
m3 <- ltm(data2pl[[3]] ~ z1)
m4 <- ltm(data2pl[[4]] ~ z1)
m5 <- ltm(data2pl[[5]] ~ z1)
```

Extract the item parameter estimates and the covariance matrices

```estm1 <- import.ltm(m1, display = FALSE)
estm2 <- import.ltm(m2, display = FALSE)
estm3 <- import.ltm(m3, display = FALSE)
estm4 <- import.ltm(m4, display = FALSE)
estm5 <- import.ltm(m5, display = FALSE)
estm1\$coef[1:3, ]
estm1\$var[1:3, 1:3]
```

Create a list of coefficients and covariance matrices

```estc <- list(estm1\$coef, estm2\$coef, estm3\$coef, estm4\$coef, estm5\$coef)
estv <- list(estm1\$var, estm2\$var, estm3\$var, estm4\$var, estm5\$var)
test <- paste("test", 1:5, sep = "")
```

Create an object of class `modIRT`

```mods <- modIRT(coef = estc, var = estv, names = test, display = FALSE)
coef(mods\$test1)[1:5]
```

```lplan<-linkp(coef = estc)
lplan
```

# Multiple equating coefficients

Estimation of the equating coefficients using the multiple mean-mean method. Form 1 is the base form.

```eqMM <- multiec(mods = mods, base = 1, method = "mean-mean")
summary(eqMM)
```

Estimation of the equating coefficients using the multiple mean-geometric mean method.

```eqMGM <- multiec(mods = mods, base = 1, method = "mean-gmean")
summary(eqMGM)
```

Estimation of the equating coefficients using the multiple item response function method.

```eqIRF<-multiec(mods = mods, base = 1, method = "irf")
summary(eqIRF)
```

Estimation of the equating coefficients using the multiple item response function method. The initial values are the estimates obtained with the multiple mean-geometric mean method.

```eqMGM <- multiec(mods = mods, base = 1, method = "mean-gmean", se = FALSE)
eqIRF<-multiec(mods = mods, base = 1, method = "irf", start = eqMGM)
summary(eqIRF)
```

Estimation of the equating coefficients using the multiple test response function method.

```eqTRF<-multiec(mods = mods, base = 1, method = "trf")
summary(eqTRF)
```

# Synthetic item parameters

The synthetic item parameters and their standard errors can be extracted as follows (using the multiple item response function method).

```eqIRF\$as
eqIRF\$bs
eqIRF\$se.as
eqIRF\$se.bs
```

# Equated scores

Equated scores with the true score equating method

```scTSE<-score(eqIRF)
round(scTSE,3)
```

Equated scores with the observed score equating method, avoiding computation of standard errors

```scOSE<-score(eqIRF, method = "OSE", se = FALSE)
round(scOSE,3)
```

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equateMultiple documentation built on Oct. 17, 2022, 5:08 p.m.