loglikelihood function for plsR models

This function provides loglikelihood computation for an univariate plsR model.

loglikpls(residpls, weights = rep.int(1, length(residpls)))

Arguments

residpls	Residuals of a fitted univariate plsR model
weights	Weights of observations

Value

real

Loglikelihood value

Details

Loglikelihood functions for plsR models with univariate response.

References

Baibing Li, Julian Morris, Elaine B. Martin, Model selection for partial least squares regression, Chemometrics and Intelligent Laboratory Systems 64 (2002) 79-89, doi: 10.1016/S0169-7439(02)00051-5 .

See also

AICpls for AIC computation and logLik for loglikelihood computations for linear models

Author

Frédéric Bertrand
frederic.bertrand@utt.fr
https://fbertran.github.io/homepage/

Examples

data(pine)
ypine <- pine[,11]
Xpine <- pine[,1:10]
(Pinscaled <- as.data.frame(cbind(scale(ypine),scale(as.matrix(Xpine)))))
#>             V1           x1           x2          x3          x4          x5
#> 1   1.93343137 -0.893800639 -0.962578437 -1.09627645 -0.43382827 -0.10494125
#> 2   0.81712282  0.206659107 -0.141067529 -0.36224787 -0.04949719  0.63880345
#> 3   0.39540626 -0.653559427 -0.141067529 -0.67683154 -1.97115262 -1.73188279
#> 4   0.04811027 -0.475315947 -0.141067529  0.68636438 -1.39465599 -1.40649448
#> 5  -0.70849886  0.322904855  0.406606409 -0.46710909 -0.72207659 -1.05786415
#> 6   0.84192968 -0.506314813 -0.277986014 -1.09627645 -0.04949719 -0.10494125
#> 7  -0.63407829  0.826636429  1.091198831  1.10580928 -1.39465599 -1.66215672
#> 8  -0.91935714 -0.049081538  2.323465192 -0.46710909  1.19957885  1.01067580
#> 9   2.71484735 -1.459529946 -0.688741468 -0.99141522 -0.91424213 -0.61626573
#> 10  0.49463369 -1.862515205  0.680443378 -0.25738664 -0.14557996 -0.75571786
#> 11 -0.53485086 -1.157291001 -0.688741468  0.58150316  1.00741330  0.33665717
#> 12 -0.13794116 -1.033295537  1.638872769  2.15442154  0.91133053  1.47551624
#> 13  2.26832393 -1.056544686 -1.921007828 -1.20113767 -1.20249045 -1.10434819
#> 14  1.53652166 -0.459816514 -1.099496921 -1.20113767  0.62308222  0.98743378
#> 15  1.16441881 -0.498565096 -0.414904499 -0.99141522 -0.24166273  0.26693110
#> 16 -0.93176057  1.710104113  1.228117316  2.04956031  1.19957885  0.59231941
#> 17 -0.84493657  1.849599011 -0.277986014  0.89608683  1.10349607  1.15012793
#> 18  0.23416169 -0.080080404  0.132769440 -0.57197032 -0.62599382  0.10423695
#> 19 -0.49764058  0.005166478  0.680443378 -0.36224787 -1.29857322 -0.89517000
#> 20 -0.11313430  0.865385012  1.365035800  0.79122561  0.14266836 -0.01197316
#> 21 -0.17515144  2.012343058 -1.236415406  2.15442154  0.71916499  0.84798165
#> 22 -0.85734000  0.632893516 -0.414904499  0.47664193 -0.24166273 -0.10494125
#> 23  0.19695141  0.477899186 -0.004149045 -0.78169277  0.81524776  1.05715985
#> 24 -0.91935714  2.004593341 -0.688741468  1.21067051  0.71916499  0.59231941
#> 25 -0.88214685  0.625143800  2.186546707  0.16205826  0.23875113 -0.01197316
#> 26 -0.16274801  0.601894650 -0.277986014 -0.67683154  0.23875113  0.70852952
#> 27 -0.84493657  0.911883311 -0.825659952  0.68636438  1.96824102  1.33606411
#> 28 -0.75811257  0.260907123 -0.688741468 -1.09627645 -1.68290430 -2.19672323
#> 29  0.34579255 -0.831802907 -0.825659952 -0.99141522 -0.91424213 -0.87192797
#> 30 -0.78291943 -0.909300072 -0.141067529  0.37178071 -0.52991104 -0.91841202
#> 31 -0.57206115 -0.676808577  0.269687924 -0.57197032  0.91133053  1.52200029
#> 32 -0.74570914 -0.669058860 -1.099496921 -0.04766419  1.29566162  0.33665717
#> 33 -0.96897085 -0.041331821  0.954280347  0.58150316  0.71916499  0.59231941
#>            x6         x7          x8          x9        x10
#> 1  -1.1025308 -2.9795617 -0.69706483 -1.02706110 -1.3713833
#> 2  -0.4055286 -0.8420501 -0.48446650 -0.49748272 -0.2009786
#> 3  -0.6843294 -0.3076721 -1.37737948 -0.85053497 -1.3713833
#> 4   0.7096750  0.2267058 -0.27186817  0.56167404 -0.5911135
#> 5  -0.5449290  0.2267058 -0.39942716 -0.32095659 -1.7615182
#> 6  -1.1025308  0.2267058 -0.73958449 -1.20358722 -1.3713833
#> 7   1.2672767  1.2954616  0.32340716  0.91472629  0.9694261
#> 8  -0.4055286 -1.9108059  0.11080883 -0.32095659 -0.5911135
#> 9  -1.1025308  0.2267058 -1.12226148 -0.85053497  0.9694261
#> 10 -0.2661281  0.7610837 -0.31438783  0.03209566  0.9694261
#> 11  0.8490754 -0.8420501  1.68403646  1.62083079 -0.2009786
#> 12  2.1036794 -1.3764280  1.59899713  1.44430467  0.9694261
#> 13 -1.1025308  0.2267058 -1.50493848 -1.55663947 -0.5911135
#> 14 -1.1025308  0.7610837 -0.73958449 -1.55663947 -1.3713833
#> 15 -0.9631303  0.2267058 -0.56950583 -1.20358722  0.1891563
#> 16  1.8248785  0.2267058  1.64151680  1.44430467  0.5792912
#> 17  1.4066772  1.2954616  0.70608415  1.26777854 -1.7615182
#> 18 -0.5449290 -2.4451838 -0.14430917  0.20862179  0.5792912
#> 19 -0.4055286  0.7610837 -1.07974182 -0.67400884  0.9694261
#> 20  0.8490754 -0.3076721  0.66356448  0.73820016  0.5792912
#> 21  1.6854781  0.2267058  0.79112348  0.91472629  0.1891563
#> 22  0.5702745 -0.3076721  0.06828916  0.38514791  0.1891563
#> 23 -0.8237299  0.7610837 -0.31438783 -0.67400884  0.5792912
#> 24  0.8490754  0.7610837  0.11080883  0.38514791  0.9694261
#> 25 -0.1267277 -0.3076721  0.11080883  0.20862179 -1.3713833
#> 26 -0.8237299  0.2267058 -0.01675017 -0.49748272  0.9694261
#> 27  1.2672767  0.7610837  2.61946911  1.26777854 -1.7615182
#> 28 -1.1025308  0.2267058 -1.67501714 -1.20358722  0.1891563
#> 29 -0.9631303  0.2267058 -0.90966315 -1.20358722  0.9694261
#> 30  0.2914737 -0.3076721 -0.05926984  1.44430467  0.9694261
#> 31 -0.6843294  0.2267058 -0.22934850 -0.85053497  0.5792912
#> 32 -0.1267277  0.7610837  1.04624148  0.56167404  0.9694261
#> 33  0.7096750  1.2954616  1.17380047  1.09125241  0.9694261
colnames(Pinscaled)[1] <- "yy"

lm(yy~x1+x2+x3+x4+x5+x6+x7+x8+x9+x10,data=Pinscaled)
#> 
#> Call:
#> lm(formula = yy ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + 
#>     x10, data = Pinscaled)
#> 
#> Coefficients:
#> (Intercept)           x1           x2           x3           x4           x5  
#>   5.034e-16   -4.601e-01   -3.175e-01    3.298e-01   -6.020e-01    5.539e-01  
#>          x6           x7           x8           x9          x10  
#>   6.720e-02   -6.054e-02    6.865e-02   -6.231e-01   -1.058e-01  
#> 

modpls <- plsR(ypine,Xpine,10)
#> ____************************************************____
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Component____ 3 ____
#> ____Component____ 4 ____
#> ____Component____ 5 ____
#> ____Component____ 6 ____
#> ____Component____ 7 ____
#> ____Component____ 8 ____
#> ____Component____ 9 ____
#> ____Component____ 10 ____
#> ____Predicting X without NA neither in X nor in Y____
#> ****________________________________________________****
#> 
modpls$Std.Coeffs
#>                  [,1]
#> Intercept  0.00000000
#> x1        -0.46014550
#> x2        -0.31750091
#> x3         0.32980012
#> x4        -0.60199305
#> x5         0.55393816
#> x6         0.06720419
#> x7        -0.06054179
#> x8         0.06864663
#> x9        -0.62312421
#> x10       -0.10578863
lm(yy~x1+x2+x3+x4+x5+x6+x7+x8+x9+x10,data=Pinscaled)
#> 
#> Call:
#> lm(formula = yy ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + 
#>     x10, data = Pinscaled)
#> 
#> Coefficients:
#> (Intercept)           x1           x2           x3           x4           x5  
#>   5.034e-16   -4.601e-01   -3.175e-01    3.298e-01   -6.020e-01    5.539e-01  
#>          x6           x7           x8           x9          x10  
#>   6.720e-02   -6.054e-02    6.865e-02   -6.231e-01   -1.058e-01  
#> 

AIC(lm(yy~x1+x2+x3+x4+x5+x6+x7+x8+x9+x10,data=Pinscaled))
#> [1] 79.37542
print(logLik(lm(yy~x1+x2+x3+x4+x5+x6+x7+x8+x9+x10,data=Pinscaled)))
#> 'log Lik.' -27.68771 (df=12)

sum(dnorm(modpls$RepY, modpls$Std.ValsPredictY, sqrt(mean(modpls$residY^2)), log=TRUE))
#> [1] -27.68771
sum(dnorm(Pinscaled$yy,fitted(lm(yy~x1+x2+x3+x4+x5+x6+x7+x8+x9+x10,data=Pinscaled)),
sqrt(mean(residuals(lm(yy~x1+x2+x3+x4+x5+x6+x7+x8+x9+x10,data=Pinscaled))^2)), log=TRUE))
#> [1] -27.68771
loglikpls(modpls$residY)
#> [1] -27.68771
loglikpls(residuals(lm(yy~x1+x2+x3+x4+x5+x6+x7+x8+x9+x10,data=Pinscaled)))
#> [1] -27.68771
AICpls(10,residuals(lm(yy~x1+x2+x3+x4+x5+x6+x7+x8+x9+x10,data=Pinscaled)))
#> [1] 79.37542
AICpls(10,modpls$residY)
#> [1] 79.37542