# Constrained Dual Scaling for Successive Categories with Groups

### Description

Uses an alternating nonnegative least squares algorithm combined with a k-means-type algorithm to optimize the constrained group dual scaling criterion outlined in the reference. Parallel computations for random starts of the grouping matrix is supported via package parallel.

### Usage

1 2 3 4 5 6 | ```
cds(x, K = 4, q = NULL, eps.ALS = 0.001, eps.G = 1e-07,
nr.starts.G = 20, nr.starts.a = 5, maxit.ALS = 20, maxit = 50,
Gstarts = NULL, astarts = NULL, parallel = FALSE, random.G = FALSE,
times.a.multistart = 1, info.level = 1, mc.preschedule = TRUE,
seed = NULL, LB = FALSE, reorder.grps = TRUE, rescale.a = TRUE,
tol = sqrt(.Machine$double.eps), update.G = TRUE)
``` |

### Arguments

`x` |
an object of class |

`K` |
The number of response style groups to look for. If a vector of
length greater than one is given, the algorithm is run for each element
and a list of class |

`q` |
The maximum rating (the scale is assumed to be |

`eps.ALS` |
Numerical convergence criterion for the alternating least squares part of the algorithm (updates for row and column scores). |

`eps.G` |
Numerical convergence criterion for the k-means part of the algorithm. |

`nr.starts.G` |
Number of random starts for the grouping matrix. |

`nr.starts.a` |
Number of random starts for the row scores. |

`maxit.ALS` |
Maximum number of iterations for the ALS part of the algorithm. A warning is given if this maximum is reached. Often it is not a concern if this maximum is reached. |

`maxit` |
Maximum number of iterations for the k-means part of the algorithm. |

`Gstarts` |
Facility to supply a list of explicit starting values for the
grouping matrix G. Each start consists of a two element list: |

`astarts` |
Supply explicit starts for the a vectors, as a list. |

`parallel` |
logical. Should parallelization over starts for the grouping matrix be used? |

`random.G` |
logical. Should the k-means part consider the individuals in a random order? |

`times.a.multistart` |
The number of times that random starts for the row scores are used. If == 1, then random starts are only used once for each start of the grouping matrix. |

`info.level` |
Verbosity of the output. Options are 1, 2, 3 and 4. |

`mc.preschedule` |
Argument to mclapply under Unix. |

`seed` |
Random seed for random number generators. Only partially implemented. |

`LB` |
logical. Load-balancing used in parallelization or not? Windows only. |

`reorder.grps` |
logical. Use the Hungarian algorithm to reorder group names so that the trace of the confusion matrix is maximized. |

`rescale.a` |
logical. Rescale row score to length sqrt(2n) if TRUE (after the algorithm has converged). |

`tol` |
tolerance |

`update.G` |
Logical indicating whether or not to update the G matrix from its starting configuration. Useful when clustering is known apriori or not desired. |

### Details

See the reference for more details.

### Value

Object of class `ds`

with elements:

`G` |
Grouping indicator matrix. |

`K` |
Number of groups K. |

`opt.crit` |
Optimum value of the criterion. |

`a` |
The 2n-vector of row scores. |

`bstar` |
The m-vector of object scores. |

`bkmat` |
The matrix of group-specific boundary scores for the ratings. |

`alphamat` |
The estimated spline coefficients for each group. |

`iter` |
The number of iterations used for the optimal random start wrt the grouping matrix. |

`time.G.start` |
The number of seconds it took for the algorithm to converge for this optimal random start. |

`grp` |
The grouping of the individuals as obtained by the algorithm. |

`kloss` |
Loss value from G update (not equivalent to that of ALS updates). |

`hitrate, confusion` |
Confusion and hitrates of original data object contained a grouping vector. |

`loss.G` |
Optimality criterion values for the random starts of G. |

`q` |
The number of ratings in the
Likert scale |

`time.total` |
Total time taken for the algorithm over all random starts |

`call` |
The function call. |

`data` |
The input data object. |

### Author(s)

Pieter C. Schoonees

### References

Schoonees, P.C., Velden, M. van de & Groenen, P.J.F. (2013). Constrained Dual Scaling for Detecting Response Styles in Categorical Data. (EI report series EI 2013-10). Rotterdam: Econometric Institute.

### Examples

1 2 3 |

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