OrdinalLogBiplotEM: Alternated EM algorithm for Ordinal Logistic Biplots
In OrdinalLogisticBiplot: Biplot representations of ordinal variables

Description Usage Arguments Value Author(s) References See Also Examples

This function computes, with an alternated algorithm, the row and column parameters of an Ordinal Logistic Biplot for ordered polytomous data. The row coordinates (E-step) are computed using multidimensional Gauss-Hermite quadratures and Expected a posteriori (EAP) scores and parameters for each variable or items (M-step) using Ridge Ordinal Logistic Regression to solve the separation problem present when the points for different categories of a variable are completely separated on the representation plane and the usual fitting methods do not converge. The separation problem is present in almost every data set for which the goodness of fit is high.

1 2	OrdinalLogBiplotEM(x,dim = 2, nnodos = 15, tol = 0.001, maxiter = 100, penalization = 0.2,show=FALSE,initial=1,alfa=1)

`x`	Matrix with the ordinal data. The matrix must be in numerical form.
`dim`	Dimension of the solution.
`nnodos`	Number of nodes for the multidimensional Gauss-Hermite quadrature.
`tol`	Value to stop the process of iterations.
`maxiter`	Maximum number of iterations in the process of solving the regression coefficients.
`penalization`	Penalization used in the diagonal matrix to avoid singularities.
`show`	Boolean parameter to specify if the user wants to see every iteration.
`initial`	Method used to choose the initial ability in the algorithm. Default value is 1.
`alfa`	Optional parameter to calculate row and column coordinates in Simple correspondence analysis if the initial parameter is equal to 1.

An object of class "ordinal.logistic.biplot.EM".This has components:

`RowCoordinates`	Coordinates for the rows or individuals
`ColumnParameters`	List with information about the Ordinal Logistic Models calculated for each variable including: estimated parameters with thresholds, percents of correct classifications,and pseudo-Rsquared
`loadings`	factor loadings
`LogLikelihood`	Logarithm of the likelihood
`r2`	R squared coefficient
`Ncats`	Number of the categories of each variable

Jose Luis Vicente-Villardon, Julio Cesar Hernandez Sanchez

Maintainer: Julio Cesar Hernandez Sanchez <juliocesar_avila@usal.es>

Bock,R. & Aitkin,M. (1981),Marginal maximum likelihood estimation of item parameters: Aplication of an EM algorithm, Phychometrika 46(4), 443-459.

pordlogist

    data(LevelSatPhd)
    dataSet = CheckDataSet(LevelSatPhd)
    datanom = dataSet$datanom
    olb = OrdinalLogBiplotEM(datanom,dim = 2, nnodos = 10,
          tol = 0.001, maxiter = 100, penalization = 0.2)
    olb

Loading required package: mirt
Loading required package: stats4
Loading required package: lattice
Loading required package: MASS
Loading required package: NominalLogisticBiplot
Loading required package: gmodels
$RowCoordinates
              [,1]        [,2]
  [1,] -0.34023661 -0.01745303
  [2,]  0.39476493 -0.33884484
  [3,] -0.40137555 -0.34180053
  [4,] -0.16594710  0.97848211
  [5,]  0.33873801  0.23839809
  [6,] -0.37210859 -0.36871369
  [7,] -0.12188081  0.24196828
  [8,] -1.08099174  0.66372740
  [9,] -0.30222754  0.32692536
 [10,]  0.28616343 -0.93041841
 [11,] -0.54961097  0.02267248
 [12,] -0.30560907 -0.33212922
 [13,]  0.33873801  0.23839809
 [14,]  0.18753954  0.46570294
 [15,]  0.18753954  0.46570294
 [16,] -0.16795236 -1.31131589
 [17,]  0.29423610  0.32755684
 [18,] -0.36203712  0.34199178
 [19,]  0.29423610  0.32755684
 [20,] -0.33659257 -0.05410977
 [21,]  1.34795221 -0.14373677
 [22,]  0.63829703 -0.91045971
 [23,] -0.33409666 -0.30518749
 [24,]  0.62681693 -0.56222809
 [25,]  0.33873801  0.23839809
 [26,]  1.34795221 -0.14373677
 [27,] -0.31762045  0.33167588
 [28,]  0.62681693 -0.56222809
 [29,]  0.33873801  0.23839809
 [30,]  0.38025252 -0.86302981
 [31,]  0.39189607 -0.01899695
 [32,]  0.08322627 -0.70558495
 [33,] -0.34023661 -0.01745303
 [34,]  0.36020350 -0.28987213
 [35,]  0.62681693 -0.56222809
 [36,] -0.35707788 -0.90033099
 [37,] -0.39677025 -0.17465457
 [38,]  0.05139888 -0.14832034
 [39,]  0.62681693 -0.56222809
 [40,]  0.36020350 -0.28987213
 [41,] -0.32137242 -0.31698001
 [42,]  0.62681693 -0.56222809
 [43,]  0.02923735  0.37419167
 [44,] -0.11385651 -0.50092887
 [45,]  0.28616343 -0.93041841
 [46,]  1.34795221 -0.14373677
 [47,]  0.36020350 -0.28987213
 [48,] -0.65713169 -0.47937472
 [49,]  1.08716281  0.18448688
 [50,]  1.02002687 -0.24948099
 [51,] -0.34603999  0.09803954
 [52,] -0.32775867 -0.50007907
 [53,]  0.33873801  0.23839809
 [54,]  0.39189607 -0.01899695
 [55,]  0.26679680 -0.47966387
 [56,] -0.33659257 -0.05410977
 [57,]  0.26679680 -0.47966387
 [58,]  0.36020350 -0.28987213
 [59,]  0.99897272 -0.57448474
 [60,]  0.41979345 -1.18164194
 [61,] -0.14750170 -0.50861607
 [62,] -0.11385651 -0.50092887
 [63,] -0.11385651 -0.50092887
 [64,]  0.89454374  0.64352608
 [65,]  0.36020350 -0.28987213
 [66,]  1.05101035  0.22081724
 [67,] -0.28037162 -0.37959951
 [68,]  0.29423610  0.32755684
 [69,]  0.36020350 -0.28987213
 [70,]  0.32428405  0.30897672
 [71,] -0.18080427 -0.78287777
 [72,]  0.33425411 -0.14894571
 [73,] -0.28037162 -0.37959951
 [74,]  0.36020350 -0.28987213
 [75,] -0.32741537 -0.18802456
 [76,] -0.19839581  0.67147704
 [77,] -0.35886761 -0.85528769
 [78,]  0.33873801  0.23839809
 [79,]  0.99897272 -0.57448474
 [80,]  0.53879523  0.25522169
 [81,] -0.91271016 -0.94002238
 [82,] -0.34538343 -0.23143838
 [83,] -1.15599111  0.07155337
 [84,]  0.32123516 -0.06615102
 [85,] -0.33659257 -0.05410977
 [86,] -1.13560503 -0.32166120
 [87,] -0.21456919  0.07388517
 [88,]  0.01379391  0.52199264
 [89,]  0.39189607 -0.01899695
 [90,]  0.62681693 -0.56222809
 [91,] -0.27684743  0.37187451
 [92,]  0.33425411 -0.14894571
 [93,] -1.11144332 -0.76578634
 [94,] -0.34603999  0.09803954
 [95,] -1.51969436  0.54000326
 [96,]  0.76207020 -0.29628080
 [97,] -0.36203712  0.34199178
 [98,] -0.37292937  0.27961753
 [99,] -0.33659257 -0.05410977
[100,]  0.33873801  0.23839809

$ColumnParameters
$ColumnParameters$coefficients
          [,1]       [,2]
[1,] -4.428062 -0.9298136
[2,] -5.913933 -3.5879863
[3,] -2.600488  2.2015307
[4,] -2.700590  6.0187289
[5,] -3.876175  2.9033437

$ColumnParameters$thresholds
           [,1]       [,2]     [,3]
[1,] -3.2882019  0.8768969 4.410132
[2,] -5.1225263 -0.2571379 3.131077
[3,] -0.4514417  0.7182389 2.675622
[4,] -1.1616634  2.3700070 4.658217
[5,] -2.7355208  1.5858225 4.888081

$ColumnParameters$fit
                      logLik  Deviance df     p-value  PCC  CoxSnell  Macfaden
Salary             -57.24320 114.48640  2 0.00000e+00 0.84 0.6691315 0.4913746
Benefits           -37.13155  74.26310  2 0.00000e+00 0.94 0.8251727 0.7013454
Job Security       -88.44406 176.88812  2 3.68594e-14 0.66 0.4613091 0.2591057
Job Location       -38.32772  76.65544  2 0.00000e+00 0.86 0.7557080 0.6477144
Working conditions -50.10089 100.20177  2 0.00000e+00 0.80 0.6884361 0.5378507
                   Nagelkerke
Salary              0.7478875
Benefits            0.9000510
Job Security        0.5079711
Job Location        0.8524633
Working conditions  0.7773554


$loadings
           [,1]       [,2]
[1,] -0.9555965 -0.2006581
[2,] -0.8461588 -0.5133650
[3,] -0.7323349  0.6199829
[4,] -0.4047525  0.9020603
[5,] -0.7838396  0.5871138

$LogLikelihood
[1] -271.2474

$r2
[1] 0.9534283 0.9795284 0.9206933 0.9775373 0.9591071

$Ncats
     [,1]
[1,]    4
[2,]    4
[3,]    4
[4,]    4
[5,]    4

attr(,"class")
[1] "ordinal.logistic.biplotEM"