Regression on principal component or discriminant scores in .NET Maker PDF 417 in .NET Regression on principal component or discriminant scores

Regression on principal component or discriminant scores use vs .net pdf417 generating tocompose pdf417 with .net ISO Standards Overview ## Principal com barcode pdf417 for .NET ponents: data frame socsupport (DAAG) ss.pr1 <- princomp(as.

matrix(na.omit(socsupport[, 9:19])), cor=TRUE) pairs(ss.pr1$scores[, 1:3]) sort(-ss.

pr1$scores[,1], decr=TRUE)[1:10] # Note the outlier ## Alternative to pairs(), using the lattice function splom() splom( ss.pr1$scores[, 1:3]). The name given w ith the point that we have identi ed as an outlier is 36 , which is the row name in the initial le. We omit this point and repeat the calculation.. <- com barcode pdf417 for .NET plete.

cases(socsupport[, 9:19])[36] <- FALSE <- princomp(as.

matrix(socsupport[, 9:19]), cor=TRUE). The output from summary() is:. > summary(ss. .net framework pdf417 pr) # Examine the contributions of the components Importance of components: Comp.

1 Comp.2 Comp.3 Comp.

4 Comp.5 Comp.6 Standard deviation 2.

394 1.219 1.137 0.

8448 0.7545 0.695 Proportion of Variance 0.

521 0.135 0.117 0.

0649 0.0517 0.044 Cumulative Proportion 0.

521 0.656 0.773 0.

8383 0.8901 0.934 Comp.

7 Comp.8 Comp.9 Comp.

10 Comp.11 Standard deviation 0.4973 0.

4561 0.3595 0.29555 0.

23189 Proportion of Variance 0.0225 0.0189 0.

0118 0.00794 0.00489 Cumulative Proportion 0.

9565 0.9754 0.9872 0.

99511 1.00000. We now regress B DI on the rst six principal components. Because the successive columns of scores are uncorrelated, the coef cients are independent. Extraneous terms that contribute little except noise will have little effect on residual mean square, and hence to the standard errors.

Thus, there is no reason to restrict the number of terms that we choose for initial examination. The coef cients in the regression output are:. > ss.lm <- barcode pdf417 for .NET lm(BDI[not.

na]$scores[, 1:6], data=socsupport) > summary(ss.lm)$coef Estimate Std.

Error t value Pr(>. t. ) (Intercept) 10 PDF-417 2d barcode for .NET .461 0.

893 11.709 3.49e-19 ss.

pr$scores[, 1:6]Comp.1 1.311 0.

373 3.513 7.23e-04 ss.

pr$scores[, 1:6]Comp.2 -0.396 0.

733 -0.540 5.91e-01 ss.

pr$scores[, 1:6]Comp.3 0.604 0.

786 0.768 4.45e-01 ss.

pr$scores[, 1:6]Comp.4 1.425 1.

058 1.347 1.82e-01 ss.

pr$scores[, 1:6]Comp.5 2.146 1.

184 1.812 7.36e-02 ss.

pr$scores[, 1:6]Comp.6 1.288 1.

285 1.003 3.19e-01.

Components other than the rst do not make an evident contribution to prediction of BDI. We now examine the loadings for the rst component:. >$loadings[, 1] emotional emotionalsat tangible tangiblesat affect 13.1 Principal component scores in regression female male 2 0 2 4 First principal component Plot of BDI against scores on the rst principal component. -0.320 affectsat -0.288 socsupport -0.

285. -0.298 psi -0.363.

-0.247 psisat -0.332.

-0.289 esupport -0.289.

-0.307 psupport -0.285.

The rst compone PDF-417 2d barcode for .NET nt is like an average of the 11 measures.1 A further step is then to plot BDI against the scores on the rst principal component, using different colors and/or different symbols for females and males.

This should be repeated for each of the other seven factors represented by columns 1 8 of the data frame socsupport. Figure 13.1 does this for the factor gender.

2 Two observations seem anomalous, with BDI indices that are high given their scores on the rst principal component. Both are females. We leave it as an exercise for the reader to recalculate the principal components with these points omitted, and repeat the regression.

Regression on principal component scores has made it possible to identify a clear effect from the social support variables. Because we have regressed on the principal components, it is not possible to ascribe these effects, with any con dence, to individual variables. The attempt to ascribe effects to individual social support variables, independently of other support variables, may anyway be misguided.

It is unlikely to re ect the reality of the way that social support variables exercise their effects.. The vector of lo adings is unique up to multiplication by 1; the presence of negative signs here is due to the nature of the algorithm. ## Plot first principal componenet score against BDI attach(socsupport) plot(BDI[] ss.

pr$scores[ ,1], col=as.numeric(gender[]), pch=as.

numeric(gender[]), xlab ="1st principal component", ylab="BDI") topleft <- par()$usr[c(1,4)] legend(topleft[1], topleft[2], col=1:2, pch=1:2, legend=levels(gender)) detach(socsupport). Regression on principal component or discriminant scores 13.2 Propensit y scores in regression comparisons labor training data A propensity is a measure, determined by explanatory variable values, of the probability that an observation will fall in the treatment rather than in the control group. Various forms of discriminant analysis may be used to determine scores.

The propensity score is intended to account for between-group differences that are not due to the effect under investigation. If there is substantial overlap between propensity scores for the different groups, then comparison of observations within the approximate region of overlap may be reasonable, but using the propensity score to adjust for differences that remain. See Rosenbaum and Rubin (1983) for further comments on the methodology.

We will rst describe the data, then investigate more conventional regression approaches to the analysis of these data, then investigate the use of propensity scores. The results highlight the dif culty in reaching secure conclusions from the use of observational data..

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