# erf: Utility fnc to compute the components for an empirical... In fungible: Psychometric Functions from the Waller Lab

 erf R Documentation

## Utility fnc to compute the components for an empirical response function

### Description

Utility function to compute empirical response functions.

### Usage

``````erf(theta, data, whichItem, min = -3, max = 3, Ncuts = 12)
``````

### Arguments

 `theta` Vector of estimated latent trait scores. `data` A matrix of binary item responses. `whichItem` Data for an erf will be generated for whichItem. `min` Default = -3. Minimum value of theta. `max` Default = 3. Maximum value of theta. `Ncuts` Number of score groups for erf.

### Value

 `probs` A vector (of length Ncuts) of bin response probabilities for the empirical response function. `centers` A vector of bin centers. `Ni` Bin sample sizes. `se.p` Standard errors of the estimated bin response probabilities.

Niels Waller

### Examples

``````
NSubj <- 2000

#generate sample k=1 FMP  data
b <- matrix(c(
#b0    b1     b2    b3      b4   b5 b6 b7  k
1.675, 1.974, -0.068, 0.053,  0,  0,  0,  0, 1,
1.550, 1.805, -0.230, 0.032,  0,  0,  0,  0, 1,
1.282, 1.063, -0.103, 0.003,  0,  0,  0,  0, 1,
0.704, 1.376, -0.107, 0.040,  0,  0,  0,  0, 1,
1.417, 1.413,  0.021, 0.000,  0,  0,  0,  0, 1,
-0.008, 1.349, -0.195, 0.144,  0,  0,  0,  0, 1,
0.512, 1.538, -0.089, 0.082,  0,  0,  0,  0, 1,
0.122, 0.601, -0.082, 0.119,  0,  0,  0,  0, 1,
1.801, 1.211,  0.015, 0.000,  0,  0,  0,  0, 1,
-0.207, 1.191,  0.066, 0.033,  0,  0,  0,  0, 1,
-0.215, 1.291, -0.087, 0.029,  0,  0,  0,  0, 1,
0.259, 0.875,  0.177, 0.072,  0,  0,  0,  0, 1,
-0.423, 0.942,  0.064, 0.094,  0,  0,  0,  0, 1,
0.113, 0.795,  0.124, 0.110,  0,  0,  0,  0, 1,
1.030, 1.525,  0.200, 0.076,  0,  0,  0,  0, 1,
0.140, 1.209,  0.082, 0.148,  0,  0,  0,  0, 1,
0.429, 1.480, -0.008, 0.061,  0,  0,  0,  0, 1,
0.089, 0.785, -0.065, 0.018,  0,  0,  0,  0, 1,
-0.516, 1.013,  0.016, 0.023,  0,  0,  0,  0, 1,
0.143, 1.315, -0.011, 0.136,  0,  0,  0,  0, 1,
0.347, 0.733, -0.121, 0.041,  0,  0,  0,  0, 1,
-0.074, 0.869,  0.013, 0.026,  0,  0,  0,  0, 1,
0.630, 1.484, -0.001, 0.000,  0,  0,  0,  0, 1),
nrow=23, ncol=9, byrow=TRUE)

theta <- rnorm(NSubj)
data<-genFMPData(NSubj = NSubj, bParam = b, theta = theta, seed = 345)\$data

erfItem1 <- erf(theta, data, whichItem = 1, min = -3, max = 3, Ncuts = 12)

plot( erfItem1\$centers, erfItem1\$probs, type="b",
main="Empirical Response Function",
xlab = expression(theta),
ylab="Probability",
cex.lab=1.5)

``````

fungible documentation built on March 31, 2023, 5:47 p.m.