#Generalized additive models are a conceptually straightforward tool that allows one to incorporate
#nonlinear predictor effects into their otherwise linear models. In addition, they allow one to keep
#within the linear and generalized linear frameworks with which one is already fa- miliar, while
#providing new avenues of model exploration and possibly improved results.
d = read.csv("http://www.nd.edu/~mclark19/learn/data/pisasci2006.csv")
library(psych)
## Warning: package 'psych' was built under R version 3.1.2
describe(d)[-1, 1:9] #univariate
## Warning in FUN(newX[, i], ...): no non-missing arguments to min; returning
## Inf
## Warning in FUN(newX[, i], ...): no non-missing arguments to max; returning
## -Inf
## vars n mean sd median trimmed mad min max
## Overall 2 57 473.14 54.58 489.00 477.45 48.93 322.00 563.00
## Issues 3 57 469.91 53.93 489.00 474.28 41.51 321.00 555.00
## Explain 4 57 475.02 54.02 490.00 478.85 47.44 334.00 566.00
## Evidence 5 57 469.81 61.74 489.00 475.11 54.86 288.00 567.00
## Interest 6 57 528.16 49.84 522.00 525.72 53.37 448.00 644.00
## Support 7 57 512.18 26.08 512.00 512.15 25.20 447.00 569.00
## Income 8 61 0.74 0.11 0.76 0.75 0.11 0.41 0.94
## Health 9 61 0.89 0.07 0.89 0.89 0.08 0.72 0.99
## Edu 10 59 0.80 0.11 0.81 0.80 0.12 0.54 0.99
## HDI 11 59 0.81 0.09 0.82 0.81 0.09 0.58 0.94
library(car)
## Warning: package 'car' was built under R version 3.1.2
##
## Attaching package: 'car'
##
## The following object is masked from 'package:psych':
##
## logit
scatterplotMatrix(d[,-c(1,3:5)],pch=19,cex=.5,reg.line=F, lwd.smooth=1.25,
spread=F,ellipse=T, col=c('gray60','#2957FF','#FF8000'), col.axis='gray50')
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lwd.smooth"
## is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lwd.smooth"
## is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lwd.smooth"
## is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lwd.smooth"
## is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lwd.smooth"
## is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lwd.smooth"
## is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lwd.smooth"
## is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lwd.smooth"
## is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lwd.smooth"
## is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lwd.smooth"
## is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lwd.smooth"
## is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lwd.smooth"
## is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.window(...): "lwd.smooth" is not a graphical parameter
## Warning in plot.xy(xy, type, ...): "lwd.smooth" is not a graphical
## parameter
## Warning in title(...): "lwd.smooth" is not a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lwd.smooth"
## is not a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "lwd.smooth"
## is not a graphical parameter
library(ggplot2); library(reshape2)
##
## Attaching package: 'ggplot2'
##
## The following object is masked from 'package:psych':
##
## %+%
## Warning: package 'reshape2' was built under R version 3.1.2
dmelt = melt(d, id=c('Country','Overall'),
measure=c('Interest','Support','Income','Health','Edu','HDI'))
head(d)
## Country Overall Issues Explain Evidence Interest Support Income
## 1 Albania NA NA NA NA NA NA 0.599
## 2 Argentina 391 395 386 385 567 506 0.678
## 3 Australia 527 535 520 531 465 487 0.826
## 4 Austria 511 505 516 505 507 515 0.835
## 5 Azerbaijan 382 353 412 344 612 542 0.566
## 6 Belgium 510 515 503 516 503 492 0.831
## Health Edu HDI
## 1 0.886 0.716 0.724
## 2 0.868 0.786 0.773
## 3 0.965 0.978 0.920
## 4 0.944 0.824 0.866
## 5 0.780 NA NA
## 6 0.935 0.868 0.877
#leave the smooth off for now
ggplot(aes(x=value,y=Overall), data=dmelt) + geom_point(color='#FF8000',alpha=.75) +
#geom_smooth(se=F) +
geom_text(aes(label=Country), alpha=.25, size=1,angle=30, hjust=-.2, vjust=-.2) +
facet_wrap(~variable, scales='free_x')
## Warning: Removed 8 rows containing missing values (geom_point).
## Warning: Removed 8 rows containing missing values (geom_point).
## Warning: Removed 11 rows containing missing values (geom_point).
## Warning: Removed 11 rows containing missing values (geom_point).
## Warning: Removed 13 rows containing missing values (geom_point).
## Warning: Removed 13 rows containing missing values (geom_point).
## Warning: Removed 8 rows containing missing values (geom_text).
## Warning: Removed 8 rows containing missing values (geom_text).
## Warning: Removed 11 rows containing missing values (geom_text).
## Warning: Removed 11 rows containing missing values (geom_text).
## Warning: Removed 13 rows containing missing values (geom_text).
## Warning: Removed 13 rows containing missing values (geom_text).
library(mgcv)
## Warning: package 'mgcv' was built under R version 3.1.2
## Loading required package: nlme
## Warning: package 'nlme' was built under R version 3.1.2
## This is mgcv 1.8-4. For overview type 'help("mgcv-package")'.
ggplot(aes(x=value,y=Overall), data=dmelt) +
geom_point(color='#FF8000',alpha=.75) +
geom_smooth(se=F, method='gam', formula=y~s(x), color='#2957FF') + facet_wrap(~variable, scales='free_x')
## Warning: Removed 8 rows containing missing values (stat_smooth).
## Warning: Removed 8 rows containing missing values (stat_smooth).
## Warning: Removed 11 rows containing missing values (stat_smooth).
## Warning: Removed 11 rows containing missing values (stat_smooth).
## Warning: Removed 13 rows containing missing values (stat_smooth).
## Warning: Removed 13 rows containing missing values (stat_smooth).
## Warning: Removed 8 rows containing missing values (geom_point).
## Warning: Removed 8 rows containing missing values (geom_point).
## Warning: Removed 11 rows containing missing values (geom_point).
## Warning: Removed 11 rows containing missing values (geom_point).
## Warning: Removed 13 rows containing missing values (geom_point).
## Warning: Removed 13 rows containing missing values (geom_point).
# ggtheme
mod_gam1 <- gam(Overall ~ s(Income, bs = "cr"), data = d)
summary(mod_gam1)
##
## Family: gaussian
## Link function: identity
##
## Formula:
## Overall ~ s(Income, bs = "cr")
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 470.444 4.082 115.3 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(Income) 6.895 7.741 16.43 1.97e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.7 Deviance explained = 73.9%
## GCV = 1053.7 Scale est. = 899.67 n = 54
plot(mod_gam1)
#AIC(mod_lm)
## [1] 550.2
#summary(mod_lm)$sp.criterion
## [1] 1504
#summary(mod_lm)$r.sq #adjusted R squared
#aic_lm aic_gam1 gcv_lm gcv_gam1 rsq_lm rsq_gam1
#550.24 529.81 1504.50 1053.73 0.52 0.70
#anova(mod_lm, mod_gam1, test = "Chisq")
#polynomial regression and GAMs
#ffects are nonlinear in the param- eters
#Response Transformation