feb9 - STA 414/2104 S: February 9 2010 Administration HW...

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STA 414/2104 S: February 9 2010 Administration I HW due February 11 by 1 pm I No class on Thursday, please bring HW to SS 2105 I Chapter 3: § 3.1, 3.2 (except 3.2.4), 3.3 (except 3.3.3), 3.4 (except 3.4.4), 3.5.1 I Chapter 4: § 4.1, 4.2, 4.3 (except 4.3.1, 4.3.2), 4.4.0, 4.4.1, 4.4.2 I Chapter 5: § 5.1, 5.2, 5.3, 5.4, 5.5, 5.7, 5.9.0 I NR office hours are Tuesday 3-4 and Thursday 2-3 I BUT, Tuesday, will be late (SGS Exam) but will stay until 5; Thursday cancelled this week 1 / 28
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STA 414/2104 S: February 9 2010 Regression splines I linear or generalized linear regression with derived feature variables I allows responses to vary “smoothly” with features, without constraining (very much) “smooth” I usual choice is to use cubic polynomials in windows of feature space, joining these continuously I with linear fits at the ends of the range of the data I fitted function (p. 146) ˆ f j ( X j ) = h j ( X j ) T ˆ θ j I note change in notation from § 5.2.1 2 / 28
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STA 414/2104 S: February 9 2010 ... regression splines I text p.146: ˆ f j ( X j ) = h j ( X j ) T ˆ θ j I previous notation (eqn. 5.2) ˆ f j ( X j ) = M j X m = 1 ˆ β jm h jm ( X j ) I in heart data example, 5 different fitted functions sbp, age, ldl, obesity, tobacco I M j 4; four derived variables for each feature I in bone density example, a single covariate (age); M 1 = 12 3 / 28
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STA 414/2104 S: February 9 2010 Figure 5.4 > plot(SAheart$sbp, heart.ns$coef[2:5]% * % + t(ns(SAheart$sbp,df=4)) 100 120 140 160 180 200 220 -2.0 -1.5 -1.0 -0.5 0.0 SAheart$sbp heart.ns$coef[2:5] %*% t(ns(SAheart$sbp, df = 4)) ˆ f ( sbp ) = h j ( sbp ) T · ˆ θ j 4 / 28
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STA 414/2104 S: February 9 2010 ... Figure 5.4 > sefhatsbp = rep(0,462) > for(j in 1:462){sefhatsbp[j] = sqrt(model.matrix(heart.ns)[j,2:5] + % * %vcov(heart.ns)[2:5,2:5]% * %model.matrix(heart.ns)[j,2:5]}) ## doesn’t reproduce Figure 5.4 Nancy Here are the commands I used to produce that plot (essentially); the actual plots were prettied up but otherwise they should be the same. Trevor
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feb9 - STA 414/2104 S: February 9 2010 Administration HW...

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