# faLocalMin: Investigate local minima in faMain objects In fungible: Psychometric Functions from the Waller Lab

## Description

Compute pairwise root mean squared deviations (RMSD) among rotated factor patterns in an `faMain` object. Prior to computing the RMSD values, each pair of solutions is aligned to the first member of the pair. Alignment is accomplished using the Hungarian algorithm as described in `faAlign`.

## Usage

 `1` ```faLocalMin(fout, Set = 1, HPthreshold = 0.1, digits = 5, PrintLevel = 1) ```

## Arguments

 `fout` (Object from class `faMain`). `Set` (Integer) The index of the solution set (i.e., the collection of rotated factor patterns with a common complexity value) from an `faMain` object. `HPthreshold` (Scalar) A number between [0, 1] that defines the hyperplane threshold. Factor pattern elements below `HPthreshold` in absolute value are counted in the hyperplane count. `digits` (Integer) Specifies the number of significant digits in the printed output. Default `digits = 5`. `PrintLevel` (Integer) Determines the level of printed output. PrintLevel = 0: No output is printed. 1: Print output for the six most discrepant pairs of rotated factor patterns. 2: Print output for all pairs of rotated factor patterns.

## Details

Compute pairwise RMSD values among rotated factor patterns from an `faMain` object.

## Value

`faLocalMin` function will produce the following output.

• rmsdTable: (Matrix) A table of `RMSD` values for each pair of rotated factor patterns in solution set `Set`.

• Set: (Integer) The index of the user-specified solution set.

• complexity.val (Numeric): The common complexity value for all members in the user-specified solution set.

• HPcount: (Integer) The hyperplane count for each factor pattern in the solution set.

## Author(s)

Niels Waller

Other Factor Analysis Routines: `BiFAD()`, `Box26`, `GenerateBoxData()`, `Ledermann()`, `SLi()`, `SchmidLeiman()`, `faAlign()`, `faEKC()`, `faIB()`, `faMB()`, `faMain()`, `faScores()`, `faSort()`, `faStandardize()`, `faX()`, `fals()`, `fapa()`, `fareg()`, `fsIndeterminacy()`, `orderFactors()`, `print.faMB()`, `print.faMain()`, `promaxQ()`, `summary.faMB()`, `summary.faMain()`
 ``` 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 34 35 36 37 38 39 40 41 42 43``` ```## Not run: ## Generate Population Model and Monte Carlo Samples #### sout <- simFA(Model = list(NFac = 5, NItemPerFac = 5, Model = "orthogonal"), Loadings = list(FacLoadDist = "fixed", FacLoadRange = .8), MonteCarlo = list(NSamples = 100, SampleSize = 500), Seed = 655342) ## Population EFA loadings (True_A <- sout\$loadings) ## Population Phi matrix sout\$Phi ## Compute EFA on Sample 67 #### fout <- faMain (R = sout\$Monte\$MCData[[67]], numFactors = 5, targetMatrix = sout\$loadings, facMethod = "fals", rotate= "cfT", rotateControl = list(numberStarts = 50, standardize="CM", kappa = 1/25), Seed=3366805) ## Summarize output from faMain summary(fout, Set = 1, DiagnosticsLevel = 2, digits=4) ## Investigate Local Solutions LMout <- faLocalMin(fout, Set = 1, HPthreshold = .15, digits= 5, PrintLevel = 1) ## Print hyperplane count for each factor pattern ## in the solution set LMout\$HPcount ## End(Not run) ```