bigen | R Documentation |

Function for generating binary data with population thresholds.

```
bigen(data, n, thresholds = NULL, Smooth = FALSE, seed = NULL)
```

`data` |
Either a matrix of binary (0/1) indicators or a correlation matrix. |

`n` |
The desired sample size of the simulated data. |

`thresholds` |
If data is a correlation matrix, thresholds must be a vector of threshold cut points. |

`Smooth` |
(logical) Smooth = TRUE will smooth the tetrachoric correltion matrix. |

`seed` |
Default = FALSE. Optional seed for random number generator. |

`data` |
Simulated binary data |

`r` |
Input or calculated (tetrachoric) correlation matrix |

Niels G Waller

```
## Example: generating binary data to match
## an existing binary data matrix
##
## Generate correlated scores using factor
## analysis model
## X <- Z *L' + U*D
## Z is a vector of factor scores
## L is a factor loading matrix
## U is a matrix of unique factor scores
## D is a scaling matrix for U
N <- 5000
# Generate data from a single factor model
# factor patter matrix
L <- matrix( rep(.707, 5), nrow = 5, ncol = 1)
# common factor scores
Z <- as.matrix(rnorm(N))
# unique factor scores
U <- matrix(rnorm(N *5), nrow = N, ncol = 5)
D <- diag(as.vector(sqrt(1 - L^2)))
# observed scores
X <- Z %*% t(L) + U %*% D
cat("\nCorrelation of continuous scores\n")
print(round(cor(X),3))
# desired difficulties (i.e., means) of
# the dichotomized scores
difficulties <- c(.2, .3, .4, .5, .6)
# cut the observed scores at these thresholds
# to approximate the above difficulties
thresholds <- qnorm(difficulties)
Binary <- matrix(0, N, ncol(X))
for(i in 1:ncol(X)){
Binary[X[,i] <= thresholds[i],i] <- 1
}
cat("\nCorrelation of Binary scores\n")
print(round(cor(Binary), 3))
## Now use 'bigen' to generate binary data matrix with
## same correlations as in Binary
z <- bigen(data = Binary, n = N)
cat("\n\nnames in returned object\n")
print(names(z))
cat("\nCorrelation of Simulated binary scores\n")
print(round(cor(z$data), 3))
cat("Observed thresholds of simulated data:\n")
cat(apply(z$data, 2, mean))
```

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