基于R语言实现LASSO回归分析

 set.seed(0820) n         <- 50 p         <- 25 beta      <- rep(0,p) beta[1:5] <- 1:5/5 X <- matrix(rnorm(n*p),n,p) X <- scale(X) Xb <- X%*%beta Y <- X%*%beta+rnorm(n) Y <- Y-mean(Y) plot(cor(X,Y),xlab="j",ylab="Cor(Y,X_j)",main="Sample correlations",cex=2)

 summary(ols)

## ## Call:## ## Residuals:##      Min       1Q   Median       3Q      Max ## -2.54540 -0.38971 -0.00738  0.49058  1.90900 ## ## Coefficients:##               Estimate Std. Error t value Pr(>|t|)    ## (Intercept) -3.914e-16  1.648e-01   0.000  1.00000    ## X1           6.020e-01  2.097e-01   2.871  0.00841 ** ## X2           5.924e-01  2.013e-01   2.944  0.00709 ** ## X3          -1.106e-01  2.290e-01  -0.483  0.63363    ## X4           1.117e+00  2.058e-01   5.427 1.42e-05 ***## X5           1.234e+00  2.190e-01   5.633 8.46e-06 ***## X6          -3.225e-01  2.322e-01  -1.389  0.17755    ## X7          -1.954e-01  2.150e-01  -0.909  0.37231    ## X8           1.466e-01  2.532e-01   0.579  0.56803    ## X9           4.678e-02  2.353e-01   0.199  0.84409    ## X10         -2.779e-01  2.151e-01  -1.292  0.20864    ## X11         -7.308e-02  2.553e-01  -0.286  0.77717    ## X12         -4.424e-02  2.642e-01  -0.167  0.86839    ## X13         -1.078e-01  2.101e-01  -0.513  0.61270    ## X14          3.000e-01  2.263e-01   1.326  0.19743    ## X15          2.396e-01  2.480e-01   0.966  0.34365    ## X16         -1.178e-01  2.285e-01  -0.515  0.61100    ## X17         -2.409e-01  2.280e-01  -1.057  0.30104    ## X18         -3.191e-01  2.396e-01  -1.332  0.19551    ## X19         -1.207e-01  2.372e-01  -0.509  0.61553    ## X20          1.721e-01  2.179e-01   0.790  0.43733    ## X21         -1.677e-02  2.144e-01  -0.078  0.93831    ## X22          3.706e-02  2.145e-01   0.173  0.86426    ## X23          3.233e-02  2.108e-01   0.153  0.87938    ## X24         -1.541e-01  2.343e-01  -0.658  0.51691    ## X25         -1.970e-01  1.965e-01  -1.002  0.32622    ## ---## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## ## Residual standard error: 1.166 on 24 degrees of freedom## Multiple R-squared:  0.8416, Adjusted R-squared:  0.6767 ## F-statistic: 5.102 on 25 and 24 DF,  p-value: 7.861e-05

 plot(lasso)

##           df       MSE      bic## Intercept  1 4.1174138 74.67329##            2 3.8224639 74.86881##            3 1.9171062 44.27691##            4 1.9136899 48.09976##            5 1.5118875 40.22806##            6 1.3016560 36.65400##            7 1.2693779 39.31051##            8 1.2124870 40.92986##            9 1.1814011 43.54326##           10 1.1728179 47.09070##           11 1.1016346 47.87201##           12 1.0050559 47.19643##           13 0.9867377 50.18875##           14 0.9636054 52.91465##           15 0.8686856 51.64164##           16 0.7777734 50.02637##           17 0.7700763 53.44111##           18 0.7663544 57.11089##           19 0.7510361 60.01336##           20 0.7451598 63.53263##           19 0.7196873 57.88151##           20 0.7149486 61.46323##           21 0.7141592 65.32002##           20 0.7051259 60.77152##           21 0.6875391 63.42065##           22 0.6764241 66.51776##           23 0.6739037 70.24313##           24 0.6570954 72.89225##           25 0.6564105 76.75213##           26 0.6520870 80.33373

 #True beta

##  [1] 0.2 0.4 0.6 0.8 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0## [18] 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

 #Estimated beta using least squares round(beta_ols,3)

##     X1     X2     X3     X4     X5     X6     X7     X8     X9    X10 ##  0.602  0.592 -0.111  1.117  1.234 -0.323 -0.195  0.147  0.047 -0.278 ##    X11    X12    X13    X14    X15    X16    X17    X18    X19    X20 ## -0.073 -0.044 -0.108  0.300  0.240 -0.118 -0.241 -0.319 -0.121  0.172 ##    X21    X22    X23    X24    X25 ## -0.017  0.037  0.032 -0.154 -0.197

 #Estimated beta using LASSO round(beta_lasso,3)

##  [1]  0.238  0.238  0.000  0.900  0.786  0.000  0.000  0.000  0.000  0.000## [11]  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000## [21]  0.000  0.000  0.000  0.000 -0.075

 #MSE - OLS mean((beta-beta_ols)^2)

## [1] 0.06204978

 #MSE - LASSO mean((beta-beta_lasso)^2)

## [1] 0.01795647