Robust Factor Analysis

Robust factor analysis are obtained by replacing the classical covariance matrix by a robust covariance estimator. This can be one of the available estimators in rrcov, i.e., MCD, OGK, M, S, SDE, or MVE estimator.

Usage

FaCov(x, ...)
# S3 method for class 'formula'
FaCov(formula, data = NULL, factors = 2, cor = FALSE, method = "mle", 
scoresMethod = "none", ...)
# Default S3 method
FaCov(x, factors = 2, cor = FALSE, cov.control = rrcov::CovControlMcd(), 
method = c("mle", "pca", "pfa"), 
scoresMethod = c("none", "regression", "Bartlett"), ...)

Arguments

x: A formula or a numeric matrix or an object that can be coerced to a numeric matrix.
...: Arguments passed to or from other methods.
formula: A formula with no response variable, referring only to numeric variables.
data: An optional data frame (or similar: see model.frame) containing the variables in the formula.
factors: The number of factors to be fitted.
cor: A logical value indicating whether the calculation should use the covariance matrix (cor = FALSE) or the correlation matrix (cor = TRUE).
method: The method of factor analysis, one of "mle" (the default), "pca", and "pfa".
scoresMethod: Type of scores to produce, if any. The default is "none", "regression" gives Thompson's scores, "Bartlett" gives Bartlett's weighted least-squares scores.
cov.control: Specifies which covariance estimator to use by providing a CovControl-class object. The default is CovControlMcd-class which will indirectly call CovMcd. If cov.control=NULL is specified, the classical estimates will be used by calling CovClassic.

Details

FaCov, serving as a constructor for objects of class FaCov-class is a generic function with "formula" and "default" methods.

Value

An S4 object of class FaCov-class which is a subclass of the virtual class Fa-class.

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

Author

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

Examples


data("hbk")
hbk.x = hbk[,1:3] 

##
## faCovPcaRegMcd is obtained from FaCov.default
##
faCovPcaRegMcd = FaCov(x = hbk.x, factors = 2, method = "pca",
scoresMethod = "regression", cov.control = rrcov::CovControlMcd()); faCovPcaRegMcd
#> An object of class "FaCov"
#> Slot "call":
#> FaCov(x = hbk.x, factors = 2, cov.control = rrcov::CovControlMcd(), 
#>     method = "pca", scoresMethod = "regression")
#> 
#> Slot "converged":
#> NULL
#> 
#> Slot "loadings":
#>        Factor1    Factor2
#> X1 -0.00357579  1.0407697
#> X2  1.01735884 -0.1074368
#> X3  0.55673070  0.4225046
#> 
#> Slot "communality":
#>        X1        X2        X3 
#> 1.0832144 1.0465617 0.4884592 
#> 
#> Slot "uniquenesses":
#>        X1        X2        X3 
#> 0.1436750 0.2022401 0.6713488 
#> 
#> Slot "cor":
#> [1] FALSE
#> 
#> Slot "covariance":
#>            X1         X2        X3
#> X1 1.22688941 0.05500588 0.1271656
#> X2 0.05500588 1.24880175 0.1525276
#> X3 0.12716557 0.15252762 1.1598081
#> 
#> Slot "correlation":
#>            X1         X2        X3
#> X1 1.00000000 0.04443853 0.1066041
#> X2 0.04443853 1.00000000 0.1267385
#> X3 0.10660407 0.12673854 1.0000000
#> 
#> Slot "usedMatrix":
#>            X1         X2        X3
#> X1 1.22688941 0.05500588 0.1271656
#> X2 0.05500588 1.24880175 0.1525276
#> X3 0.12716557 0.15252762 1.1598081
#> 
#> Slot "reducedCorrelation":
#> NULL
#> 
#> Slot "criteria":
#> NULL
#> 
#> Slot "factors":
#> [1] 2
#> 
#> Slot "dof":
#> NULL
#> 
#> Slot "method":
#> [1] "pca"
#> 
#> Slot "scores":
#>           Factor1     Factor2
#>  [1,] 23.37446110 12.08300643
#>  [2,] 24.34703619 11.62237670
#>  [3,] 24.83571062 13.27852593
#>  [4,] 26.17084132 12.61905004
#>  [5,] 25.59918577 12.83553071
#>  [6,] 24.28522312 12.79892797
#>  [7,] 24.65518678 12.44282588
#>  [8,] 23.58356104 12.06537192
#>  [9,] 25.29871081 12.37449155
#> [10,] 24.28794072 11.99663283
#> [11,] 29.29010377 14.10292664
#> [12,] 29.21602329 15.67548601
#> [13,] 30.36694090 14.31639870
#> [14,] 36.61093166 12.22469826
#> [15,]  0.87846757  1.48055428
#> [16,] -0.33469848  0.81353359
#> [17,] -0.59533115 -1.67797608
#> [18,] -0.07692585  0.74960673
#> [19,]  0.88664992 -0.81140980
#> [20,]  1.32586314  1.18338691
#> [21,]  0.32355720  0.87258307
#> [22,]  1.26507774 -1.10045701
#> [23,]  0.02132206  0.03769255
#> [24,] -0.04050523 -0.62810919
#> [25,] -1.82877805 -0.54081595
#> [26,]  1.53565293 -0.52706006
#> [27,]  0.88763579  1.69714971
#> [28,] -0.65476444  0.46386279
#> [29,] -0.99571552 -0.40049510
#> [30,] -0.14326046  0.39732743
#> [31,] -0.68032580  1.14648951
#> [32,]  0.02122339 -1.36276478
#> [33,]  0.94777315 -0.29514861
#> [34,] -1.66606969 -0.94732785
#> [35,]  0.86479203  1.57748129
#> [36,]  0.74968605 -0.12896299
#> [37,]  1.40520991 -1.10997137
#> [38,] -1.02005187 -0.37734893
#> [39,] -1.60441131  0.60226525
#> [40,]  0.06134748 -1.03421632
#> [41,]  0.18615684  1.92215530
#> [42,] -0.11319178 -0.59882173
#> [43,]  0.97827831 -1.65842318
#> [44,] -0.42141261  0.86497778
#> [45,] -1.74410700  0.24465420
#> [46,] -0.49884452  0.80604306
#> [47,] -1.75203599  1.21093123
#> [48,]  0.24815304  1.70416567
#> [49,]  0.51599641  1.23750475
#> [50,]  1.21199639  0.65981510
#> [51,] -0.77346099  0.29396447
#> [52,] -1.23505304  1.49707994
#> [53,] -0.34337530 -0.32700427
#> [54,]  0.43714215 -0.96286408
#> [55,]  0.25351912 -1.18596060
#> [56,]  0.76927705 -0.24033134
#> [57,] -1.23515172  0.09662262
#> [58,]  1.10917203  0.39971572
#> [59,]  0.74995363  0.38770297
#> [60,]  0.50450331 -0.50119529
#> [61,]  1.84511298 -0.80798712
#> [62,] -1.78265404 -0.66860453
#> [63,]  0.16718657 -0.94482480
#> [64,]  1.31183557  1.20554365
#> [65,] -0.47635280  0.85094120
#> [66,] -0.22439584 -1.36787167
#> [67,] -0.02401342 -0.12687401
#> [68,] -1.48792563 -1.07691539
#> [69,] -1.48261557  0.15956004
#> [70,]  0.83487804 -0.15251392
#> [71,]  0.74070096  0.61300322
#> [72,]  0.16973526 -0.86332857
#> [73,]  0.23278757 -0.85700738
#> [74,]  0.40917146 -1.36044628
#> [75,] -0.61438698 -0.53327581
#> 
#> Slot "scoresMethod":
#> [1] "regression"
#> 
#> Slot "scoringCoef":
#>                  X1         X2        X3
#> Factor1 -0.07760082  0.7707987 0.3871595
#> Factor2  0.82485664 -0.1583555 0.2946736
#> 
#> Slot "meanF":
#>  Factor1  Factor2 
#> 4.958958 2.405817 
#> 
#> Slot "corF":
#>           Factor1   Factor2
#> Factor1 1.0000000 0.9730208
#> Factor2 0.9730208 1.0000000
#> 
#> Slot "STATISTIC":
#> NULL
#> 
#> Slot "PVAL":
#> NULL
#> 
#> Slot "n.obs":
#> [1] 75
#> 
#> Slot "center":
#>       X1       X2       X3 
#> 1.537705 1.780328 1.686885 
#> 
#> Slot "eigenvalues":
#> [1] 1.436470 1.181766 1.017264
#> 
#> Slot "cov.control":
#> An object of class "CovControlMcd"
#> Slot "alpha":
#> [1] 0.5
#> 
#> Slot "nsamp":
#> [1] 500
#> 
#> Slot "scalefn":
#> NULL
#> 
#> Slot "maxcsteps":
#> [1] 200
#> 
#> Slot "seed":
#> NULL
#> 
#> Slot "use.correction":
#> [1] TRUE
#> 
#> Slot "trace":
#> [1] FALSE
#> 
#> Slot "tolSolve":
#> [1] 1e-14
#> 
#> 

##
## In fact, it is equivalent to use FaCov.formula
## faCovForPcaRegMcd = faCovPcaRegMcd
##
faCovForPcaRegMcd = FaCov(~., data = as.data.frame(hbk.x), 
factors = 2, method = "pca", scoresMethod = "regression", 
cov.control = rrcov::CovControlMcd()); faCovForPcaRegMcd
#> An object of class "FaCov"
#> Slot "call":
#> FaCov(formula = ~., data = as.data.frame(hbk.x), factors = 2, 
#>     method = "pca", scoresMethod = "regression", cov.control = rrcov::CovControlMcd())
#> 
#> Slot "converged":
#> NULL
#> 
#> Slot "loadings":
#>        Factor1    Factor2
#> X1 -0.00357579  1.0407697
#> X2  1.01735884 -0.1074368
#> X3  0.55673070  0.4225046
#> 
#> Slot "communality":
#>        X1        X2        X3 
#> 1.0832144 1.0465617 0.4884592 
#> 
#> Slot "uniquenesses":
#>        X1        X2        X3 
#> 0.1436750 0.2022401 0.6713488 
#> 
#> Slot "cor":
#> [1] FALSE
#> 
#> Slot "covariance":
#>            X1         X2        X3
#> X1 1.22688941 0.05500588 0.1271656
#> X2 0.05500588 1.24880175 0.1525276
#> X3 0.12716557 0.15252762 1.1598081
#> 
#> Slot "correlation":
#>            X1         X2        X3
#> X1 1.00000000 0.04443853 0.1066041
#> X2 0.04443853 1.00000000 0.1267385
#> X3 0.10660407 0.12673854 1.0000000
#> 
#> Slot "usedMatrix":
#>            X1         X2        X3
#> X1 1.22688941 0.05500588 0.1271656
#> X2 0.05500588 1.24880175 0.1525276
#> X3 0.12716557 0.15252762 1.1598081
#> 
#> Slot "reducedCorrelation":
#> NULL
#> 
#> Slot "criteria":
#> NULL
#> 
#> Slot "factors":
#> [1] 2
#> 
#> Slot "dof":
#> NULL
#> 
#> Slot "method":
#> [1] "pca"
#> 
#> Slot "scores":
#>        Factor1     Factor2
#> 1  23.37446110 12.08300643
#> 2  24.34703619 11.62237670
#> 3  24.83571062 13.27852593
#> 4  26.17084132 12.61905004
#> 5  25.59918577 12.83553071
#> 6  24.28522312 12.79892797
#> 7  24.65518678 12.44282588
#> 8  23.58356104 12.06537192
#> 9  25.29871081 12.37449155
#> 10 24.28794072 11.99663283
#> 11 29.29010377 14.10292664
#> 12 29.21602329 15.67548601
#> 13 30.36694090 14.31639870
#> 14 36.61093166 12.22469826
#> 15  0.87846757  1.48055428
#> 16 -0.33469848  0.81353359
#> 17 -0.59533115 -1.67797608
#> 18 -0.07692585  0.74960673
#> 19  0.88664992 -0.81140980
#> 20  1.32586314  1.18338691
#> 21  0.32355720  0.87258307
#> 22  1.26507774 -1.10045701
#> 23  0.02132206  0.03769255
#> 24 -0.04050523 -0.62810919
#> 25 -1.82877805 -0.54081595
#> 26  1.53565293 -0.52706006
#> 27  0.88763579  1.69714971
#> 28 -0.65476444  0.46386279
#> 29 -0.99571552 -0.40049510
#> 30 -0.14326046  0.39732743
#> 31 -0.68032580  1.14648951
#> 32  0.02122339 -1.36276478
#> 33  0.94777315 -0.29514861
#> 34 -1.66606969 -0.94732785
#> 35  0.86479203  1.57748129
#> 36  0.74968605 -0.12896299
#> 37  1.40520991 -1.10997137
#> 38 -1.02005187 -0.37734893
#> 39 -1.60441131  0.60226525
#> 40  0.06134748 -1.03421632
#> 41  0.18615684  1.92215530
#> 42 -0.11319178 -0.59882173
#> 43  0.97827831 -1.65842318
#> 44 -0.42141261  0.86497778
#> 45 -1.74410700  0.24465420
#> 46 -0.49884452  0.80604306
#> 47 -1.75203599  1.21093123
#> 48  0.24815304  1.70416567
#> 49  0.51599641  1.23750475
#> 50  1.21199639  0.65981510
#> 51 -0.77346099  0.29396447
#> 52 -1.23505304  1.49707994
#> 53 -0.34337530 -0.32700427
#> 54  0.43714215 -0.96286408
#> 55  0.25351912 -1.18596060
#> 56  0.76927705 -0.24033134
#> 57 -1.23515172  0.09662262
#> 58  1.10917203  0.39971572
#> 59  0.74995363  0.38770297
#> 60  0.50450331 -0.50119529
#> 61  1.84511298 -0.80798712
#> 62 -1.78265404 -0.66860453
#> 63  0.16718657 -0.94482480
#> 64  1.31183557  1.20554365
#> 65 -0.47635280  0.85094120
#> 66 -0.22439584 -1.36787167
#> 67 -0.02401342 -0.12687401
#> 68 -1.48792563 -1.07691539
#> 69 -1.48261557  0.15956004
#> 70  0.83487804 -0.15251392
#> 71  0.74070096  0.61300322
#> 72  0.16973526 -0.86332857
#> 73  0.23278757 -0.85700738
#> 74  0.40917146 -1.36044628
#> 75 -0.61438698 -0.53327581
#> 
#> Slot "scoresMethod":
#> [1] "regression"
#> 
#> Slot "scoringCoef":
#>                  X1         X2        X3
#> Factor1 -0.07760082  0.7707987 0.3871595
#> Factor2  0.82485664 -0.1583555 0.2946736
#> 
#> Slot "meanF":
#>  Factor1  Factor2 
#> 4.958958 2.405817 
#> 
#> Slot "corF":
#>           Factor1   Factor2
#> Factor1 1.0000000 0.9730208
#> Factor2 0.9730208 1.0000000
#> 
#> Slot "STATISTIC":
#> NULL
#> 
#> Slot "PVAL":
#> NULL
#> 
#> Slot "n.obs":
#> [1] 75
#> 
#> Slot "center":
#>       X1       X2       X3 
#> 1.537705 1.780328 1.686885 
#> 
#> Slot "eigenvalues":
#> [1] 1.436470 1.181766 1.017264
#> 
#> Slot "cov.control":
#> An object of class "CovControlMcd"
#> Slot "alpha":
#> [1] 0.5
#> 
#> Slot "nsamp":
#> [1] 500
#> 
#> Slot "scalefn":
#> NULL
#> 
#> Slot "maxcsteps":
#> [1] 200
#> 
#> Slot "seed":
#> NULL
#> 
#> Slot "use.correction":
#> [1] TRUE
#> 
#> Slot "trace":
#> [1] FALSE
#> 
#> Slot "tolSolve":
#> [1] 1e-14
#> 
#>