Statistik
eksempler i R

Neurologi Neuroanatomi Statistik Home

Deskriptiv

Kvantitative data
Kategoriske data
Intervaller

Analytisk

Sandsynligheder

Kategoriske udfald

Kategoriske eksponeringer
Logistisk regression

Kvantitative udfald

Kvantitative udfald
Linær regression
Korrelationer
Overlevelse
Poisson regression

Tilfældighed

Randomisering

Forskning

PhD thesis



Jacob Liljehult
Klinisk sygeplejespecialist
cand.scient.san, Ph.d.

Neurologisk afdeling
Nordsjællands Hospital

Linær regression

Simpel linær model

model1 <- lm(weight ~ age, data = strokedata)
summary(model1)

Call:
lm(formula = weight ~ age, data = apodata)

Residuals:
Min1Q Median3QMax
-40.138 -12.137 -1.291 10.901102.555
Coefficients:
EstimateStd. Error t valuePr(>|t|)
(Intercept) 102.375813.17603 32.234<2e-16 ***
age -0.38471 0.04363-8.818<2e-16***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 16.87 on 981 degrees of freedom
(48 observations deleted due to missingness)
Multiple R-squared: 0.07344, Adjusted R-squared: 0.07249
F-statistic: 77.75 on 1 and 981 DF, p-value: < 2.2e-16

Justeret model

model2 <- lm(weight ~ age + height, data = strokedata)
summary(model2)

Call:
lm(formula = weight ~ age + height, data = strokedata)

Residuals:
Min 1Q Median 3Q Max
-46.578 -8.662 -1.524 7.137 98.136
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -79.61793 9.76465-8.1541.08e-15 ***
age-0.15257 0.03902 -3.910 9.88e-05 ***
height 0.96616 0.0498219.394 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 14.36 on 978 degrees of freedom
(50 observations deleted due to missingness)
Multiple R-squared: 0.3307, Adjusted R-squared: 0.3293
F-statistic: 241.6 on 2 and 978 DF, p-value: < 2.2e-16

Goodness of fit

mf1 <- strokedata %>% select(age, weight, height) %>%
filter(!is.na(age) & !is.na(weight) & !is.na(height))
md1 <- lm(weight ~ age, data = mf1)
md2 <- lm(weight ~ age + height, data = mf1)
anova(md1,md2)

Analysis of Variance Table

Model 1: weight ~ age
Model 2: weight ~ age + height
Res.Df RSS Df Sum of Sq FPr(>F)
1 979 279134
2 978 201599 1 77535 376.14 <2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Kontrol af modelantagelser

Kontrol af linearitet

scatter.smooth(strokedata$age, resid(model1))
abline(0,0,col = "red", lty=2)

Error in xy.coords(x, y, xlabel, ylabel) : 'x' and 'y' lengths differ

scatter.smooth(subset(strokedata$age, !is.na(strokedata$weight)), resid(model1))
abline(0,0,col = "red", lty=2)

plot(model1, which = 1)

Normalfordeling af residualer

par(mfrow = c(2,1))
plot(model1, which = 2)
hist(residuals(model1))

Varianshomogenitet

plot(model1, which = 3)

Eksempel på model hvor antagelserne ikke er opfyldt

model3 <- lm(sss ~ age, data = strokedata)
summary(model3)

Call:
lm(formula = sss ~ age, data = strokedata)

Residuals:
Min 1Q Median 3Q Max
-52.069 -6.159 4.700 10.405 20.290
Coefficients:
EstimateStd. Error t value Pr(>|t|)
(Intercept) 69.66015 2.6523826.263 <2e-16 ***
age -0.35899 0.03638 -9.869 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 14.5 on 1029 degrees of freedom
Multiple R-squared: 0.08647, Adjusted R-squared: 0.08558
F-statistic: 97.4 on 1 and 1029 DF, p-value: < 2.2e-16

library(ggplot2)
ggplot(aes(x = age, y = sss), data = apodata) + geom_point() +
geom_smooth(method = loess) + theme_bw()

par(mfrow = c(5,1))
scatter.smooth(strokedata$age, resid(model3))
abline(0,0,col = "red", lty=2)
plot(model3, which = 1)
plot(model3, which = 2)
hist(residuals(model3))
plot(model3, which = 3)