Model-based Sliced Inverse Regression directions

MSIR estimates a set of \(d \le p\) orthogonal direction vectors of length \(p\) which are estimates of the basis of the dimensional reduction subspace.

Usage

# S3 method for class 'msir'
predict(object, dim = 1:object$numdir, newdata, ...)

Arguments

object: an object of class 'msir' resulting from a call to msir.
dim: the dimensions of the reduced subspace used for prediction.
newdata: a data frame or matrix giving the data. If missing the data obtained from the call to msir are used.
...: further arguments passed to or from other methods.

Value

The function returns a matrix of points projected on the subspace spanned by the estimated basis vectors.

References

Scrucca, L. (2011) Model-based SIR for dimension reduction. Computational Statistics & Data Analysis, 55(11), 3010-3026.

Author

Luca Scrucca luca.scrucca@unipg.it

Examples

n <- 200
p <- 5
b <- as.matrix(c(1,-1,rep(0,p-2)))
x <- matrix(rnorm(n*p), nrow = n, ncol = p)
y <- exp(0.5 * x%*%b) + 0.1*rnorm(n)
pairs(cbind(y,x), gap = 0)


MSIR <- msir(x, y)
summary(MSIR)
#> -------------------------------------------------- 
#> Model-based SIR 
#> -------------------------------------------------- 
#> 
#> Slices:
#>           1   2   3    4    5   6    
#> GMM       XII XXX VVE  VEE  XXX EEI  
#> Num.comp. 1   1   2    2    1   2    
#> Num.obs.  33  33  26|7 24|9 33  10|25
#> 
#> Estimated basis vectors:
#>          Dir1     Dir2      Dir3      Dir4     Dir5
#> x1  0.7024558  0.60839  0.203601  0.143848 -0.15454
#> x2 -0.7109685  0.73510  0.243302  0.058432 -0.16883
#> x3 -0.0138463  0.02881 -0.219786  0.898336  0.40682
#> x4  0.0284116  0.25696 -0.095483 -0.390935  0.83908
#> x5 -0.0089805 -0.15045  0.917566  0.126713  0.27939
#> 
#>                 Dir1    Dir2     Dir3      Dir4       Dir5
#> Eigenvalues  0.91359  0.1859  0.11066  0.025298   0.010362
#> Cum. %      73.33299 88.2549 97.13761 99.168286 100.000000
plot(MSIR, which = 1, type = "2Dplot")

all.equal(predict(MSIR), MSIR$dir)
#> [1] TRUE
predict(MSIR, dim = 1:2)
#>                Dir1        Dir2
#>   [1,] -0.583271363  0.05688139
#>   [2,]  0.586516915  0.56464628
#>   [3,]  0.699109331 -1.16039645
#>   [4,]  0.937829896  1.04407785
#>   [5,] -0.493455003 -0.34953621
#>   [6,] -0.359065898  1.14710930
#>   [7,]  1.330409511  1.12217253
#>   [8,] -0.423727960  0.36222116
#>   [9,]  0.802568179  0.43392210
#>  [10,]  0.695395427 -1.55265524
#>  [11,] -0.242717397 -0.50580893
#>  [12,]  0.182375341  1.16425896
#>  [13,] -0.288503067 -0.45526593
#>  [14,] -1.319233133 -0.53060600
#>  [15,] -0.451156643  0.59995440
#>  [16,] -1.239580301  0.39098189
#>  [17,] -0.450268305  0.64039001
#>  [18,]  0.097901344  1.64349029
#>  [19,] -1.510104433 -0.65141765
#>  [20,]  0.121471319 -0.73652092
#>  [21,]  1.013800786  0.25763761
#>  [22,]  0.970833515 -0.32707651
#>  [23,] -0.709765388 -0.90006587
#>  [24,] -0.211860946  0.24875593
#>  [25,] -1.614840965 -1.15344493
#>  [26,]  0.693133873  0.80544809
#>  [27,]  1.023467949  0.01467181
#>  [28,] -0.767290428  0.66126261
#>  [29,]  0.984169413  0.06826555
#>  [30,] -0.148786759  1.22726009
#>  [31,] -0.466950022 -0.43604705
#>  [32,] -0.276215479 -1.37250226
#>  [33,] -0.204917287  0.74558961
#>  [34,] -1.078072340  0.01866589
#>  [35,] -0.920395261  1.01956358
#>  [36,] -0.915800581 -1.54084696
#>  [37,] -0.693038836  0.43915095
#>  [38,] -1.199194594  0.08773774
#>  [39,] -0.288585981  0.08518980
#>  [40,]  0.038148520 -0.73524861
#>  [41,] -2.168536044  0.70025456
#>  [42,] -0.393914044  0.17624971
#>  [43,]  0.369148995 -0.21478389
#>  [44,]  1.192539864  2.36173436
#>  [45,] -0.157775809 -1.47500209
#>  [46,]  0.524271746 -1.28603824
#>  [47,] -0.106183133  0.31389282
#>  [48,] -0.030681741 -0.63581565
#>  [49,] -0.436660779 -0.87167418
#>  [50,]  1.613320295  0.07198957
#>  [51,] -1.882619496  0.10637585
#>  [52,]  0.745185537  0.49521511
#>  [53,]  0.602763903  0.91001074
#>  [54,]  0.849377675 -0.72210774
#>  [55,] -1.490078985 -0.44144178
#>  [56,]  0.313481370  0.33000405
#>  [57,]  0.028067960 -1.34377906
#>  [58,] -0.501069876  0.99810947
#>  [59,] -0.340520773 -0.84248735
#>  [60,]  0.744628603 -0.68202959
#>  [61,]  1.596456505 -1.36862889
#>  [62,] -0.258845243 -1.08286262
#>  [63,] -0.454829136  0.48699149
#>  [64,]  1.153539143  1.01917184
#>  [65,]  0.924838793  0.41253203
#>  [66,] -2.322841280 -0.89871862
#>  [67,]  0.320918787 -0.21534053
#>  [68,]  0.510590773  0.17197063
#>  [69,] -0.120961441  0.77809691
#>  [70,]  0.940629711  0.11361708
#>  [71,]  0.243860115  1.92671458
#>  [72,] -0.460077602 -1.50040147
#>  [73,] -1.926644966  0.25066780
#>  [74,]  0.955698290 -1.62860734
#>  [75,] -0.400811934 -0.38629999
#>  [76,] -0.575173779  1.31268431
#>  [77,]  1.422580762  1.86052819
#>  [78,]  0.184035924 -0.52071997
#>  [79,]  1.288763017 -0.26158648
#>  [80,] -0.413025620  1.80285442
#>  [81,]  0.431206664  0.98966930
#>  [82,] -0.286372505  0.09767694
#>  [83,] -0.643692755  0.38850690
#>  [84,] -0.429324629  0.21704218
#>  [85,]  0.794951124 -0.45172986
#>  [86,]  0.815781992  1.02932777
#>  [87,] -0.198754693 -0.55480912
#>  [88,] -0.176530367 -0.19465334
#>  [89,] -0.193920887  1.85173190
#>  [90,] -0.234155715 -1.23009258
#>  [91,] -0.534248539  0.72433894
#>  [92,]  0.775276092  1.78999757
#>  [93,]  0.035398478  0.02890304
#>  [94,]  1.697483153 -0.50628344
#>  [95,] -0.400100327 -1.34443492
#>  [96,]  0.610477537  0.40216872
#>  [97,]  0.778450348  0.29607754
#>  [98,] -0.185846797  1.10302507
#>  [99,] -0.879495250 -0.43701955
#> [100,]  0.140985421 -0.26204738
#> [101,]  1.484319316 -0.58197726
#> [102,]  0.987905696 -0.65012066
#> [103,] -0.310981454 -0.56589957
#> [104,] -0.774241786 -0.17913685
#> [105,] -2.084346320 -0.55719006
#> [106,]  1.582605211  0.03222398
#> [107,]  0.307364901  0.67784947
#> [108,]  0.784596851  0.43626348
#> [109,]  1.205704066 -0.95099627
#> [110,]  0.793710878 -0.71730750
#> [111,] -1.907932390  0.14691415
#> [112,] -1.095750684 -0.76234024
#> [113,] -0.900259602  1.49338506
#> [114,] -0.816804502  0.96292933
#> [115,]  1.473543505 -1.61551760
#> [116,]  0.078747061 -0.06960531
#> [117,]  0.642291981  1.67885306
#> [118,] -0.238963209 -0.05974026
#> [119,] -1.605732427  0.14829398
#> [120,] -0.010193861 -0.33598292
#> [121,]  0.144361463  1.08607720
#> [122,]  1.886419530  1.72542529
#> [123,]  1.014012248 -0.20356495
#> [124,]  0.273413677 -2.04367287
#> [125,] -1.315607595  0.39981105
#> [126,] -0.743131843 -0.37018605
#> [127,] -0.007237442 -0.22412631
#> [128,] -0.764130015 -0.20078857
#> [129,] -2.120001507 -1.56242054
#> [130,] -1.733704150 -0.01445850
#> [131,] -1.709039931  0.56635421
#> [132,]  0.658417485 -0.52517562
#> [133,]  1.631021528  2.08925394
#> [134,]  1.195855732 -2.31633055
#> [135,] -0.386635876  0.19096398
#> [136,] -1.306508911 -1.03641886
#> [137,] -0.420531653  0.48357565
#> [138,] -1.245382212 -1.19583156
#> [139,]  0.826351319  0.26691919
#> [140,] -1.584635926  1.04465707
#> [141,] -0.101246357 -1.75317318
#> [142,] -0.713941520 -0.85256027
#> [143,] -0.907330526 -0.15258507
#> [144,]  1.421239780 -0.84117917
#> [145,] -0.378477885 -2.83868951
#> [146,] -0.059002336 -1.68587410
#> [147,]  0.422796417  1.28623444
#> [148,] -0.008865249  0.08427358
#> [149,]  1.829741124 -0.37866324
#> [150,] -1.008990831  0.02514176
#> [151,]  1.312591712 -1.38508933
#> [152,]  2.122514213 -0.37671431
#> [153,]  0.571297808 -1.35429558
#> [154,]  1.183077850 -0.22320222
#> [155,]  1.574760690 -0.28406244
#> [156,] -0.103041393 -1.33494187
#> [157,] -0.420545907  0.75879303
#> [158,]  0.125006087  0.45097160
#> [159,] -0.393752823  0.80215524
#> [160,]  0.036364758  1.85103334
#> [161,]  0.400211171  0.19471644
#> [162,]  0.578891188 -1.73973684
#> [163,] -0.186025865  0.59813351
#> [164,]  0.348594221  1.40388854
#> [165,]  0.038085308 -0.31955426
#> [166,]  0.605969809  1.33117408
#> [167,]  0.444419199  0.52584894
#> [168,] -1.379862600 -1.27741931
#> [169,] -0.056821104 -0.86626821
#> [170,] -1.223372266  1.59320560
#> [171,]  1.405640709  0.75353976
#> [172,]  0.259835211 -0.04021414
#> [173,]  0.520746039 -0.53698067
#> [174,]  0.540822087  0.69264423
#> [175,] -1.267341097 -0.25557397
#> [176,]  0.216859016  0.73989930
#> [177,]  0.154431141  0.40614635
#> [178,] -1.300568148  0.76851631
#> [179,]  1.647141169 -0.74334415
#> [180,] -0.264899204 -1.05463610
#> [181,]  0.550844359  1.10278589
#> [182,] -0.972680103 -0.50082033
#> [183,]  0.952827628  0.04996772
#> [184,] -0.180983276 -0.67138241
#> [185,] -0.287480567 -0.23858259
#> [186,]  0.796551982 -1.27915220
#> [187,] -1.204101426 -0.31368249
#> [188,]  1.129163684 -1.35540815
#> [189,] -0.945173433  1.84319589
#> [190,]  0.055320420 -0.24531869
#> [191,]  0.740838361 -0.91502720
#> [192,]  1.124476387  1.42781091
#> [193,]  0.846308738 -1.36608548
#> [194,] -0.037386104 -0.67611049
#> [195,] -0.079879074  0.89628912
#> [196,] -0.917128583  1.82687772
#> [197,] -1.630431451  2.48800752
#> [198,]  0.749864980  0.96528475
#> [199,]  0.101180543 -0.79549045
#> [200,]  0.010678804  0.49371996

x0 <- matrix(rnorm(n*p), nrow = n, ncol = p)
y0 <- exp(0.5 * x0%*%b) + 0.1*rnorm(n)
plot(predict(MSIR, dim = 1, newdata = x0), y0)