# fs.msa.n1: Determining n1 for the Forward Search for Mokken Scale... In fwdmsa: Forward search for Mokken scale analysis

## Description

Computes n1 for the Forward Search for Mokken scale analysis

## Usage

 ```1 2 3 4 5 6 7 8``` ```fs.MSA.n1( X, B, cutoff = default.cutoff, initial.subsample.size = default.initial.subsample.size, minsize = default.minsize, seed = default.seed, verbose = TRUE) ```

## Arguments

 `X` Matrix or data frame of numeric data containing the responses of `nrow(X)` respondents to `ncol(X)` items. Each row is called an observation. Each item has m+1 response options 0, …, m. Other scores (e.g., 1, …, m+1), are converted to 0, …, m. Missing values are not allowed. `B` Integer giving the number of Forward Searches with different initial subsamples. `cutoff` Integer, the first step of the Forward Search for which the number of unique subsamples is below the `cutoff` equals n1. `initial.subsample.size` Integer giving the size of the initial subsample. By default `initial.subsample.size` equals the minimum of the number of restscore groups over all items multiplied by the number of items. `minsize` Integer giving the minimum size of a rest score group. By default `minsize` = N/10 if N ≥ 500; `minsize` = N/5 if 250 ≤ N < 500; and `minsize` = max(N/3,50) if N < 250 `seed` Numeric; fixes the random number generation `set.seed` in order to control the initial subsample. Default is a randomly drawn value between 1 and 10000. `verbose` Logical, indicating whether `B` should be printed on the screen. If `FALSE`, no output is produced. The default is `TRUE`.

## Details

Function `fs.MSA.n1` computes the required input for the forward plot (`plot.fs.n1.class`). Therefore, its values should be assigned to an object. `B` should at least be larger than `cutoff`, preferably `B`≥ 100. Large values of `B` may take much computation time.

## Value

`number.unique.subsamples`. The number of unique subsamples at each step of the Forward Search.
`n1`. The first step for which the number of unique subsamples is below the cutoff.

## Author(s)

W. P. Zijlstra w.p.zijlstra@uvt.nl

## References

Zijlstra, W. P., Van der Ark, L. A., and Sijtsma, K. (2011). Robust Mokken scale analysis by means of the forward search algorithm for outlier detection. Multivariate Behavioral Research, 46, 58-89.

`plot.fs.n1.class`, `fs.MSA`, `plot.fs.class`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```## Not run: ## Retrieve data (588 observations) data(acs) # Determine n1 by running the Forward Search for Mokken scale analysis # B=100 times fwdmsa.res.n1 <- fs.MSA.n1(acs, B=100) # Plot of number unique subsamples plot(fwdmsa.res.n1) ## End(Not run) ```