April13

Galton<-read.csv("http://www.cknudson.com/data/Galton.csv")
attach(Galton)
names(Galton)

## [1] "FamilyID"     "FatherHeight" "MotherHeight" "Gender"       "Height"      
## [6] "NumKids"

1. How many kids were part of the study? 898

2. What is our primary sampling unit? Family

3. What are the elements? Children

4. What kind of correlation structure do we have? Repeated measures

5. In the context of this study, what does intraclass correlation measure? Measures similarity between siblings

6. ‘Gender’ defines our fixed effects (2)

7. ‘FamilyID’ defines our random effects

8. 197 random effects

fixedmod<-lm(Height~0+Gender, data=Galton)
library(lme4)

## Loading required package: Matrix

mixedmod<-lmer(Height~0+Gender + (1|FamilyID), data=Galton)
summary(fixedmod)

## 
## Call:
## lm(formula = Height ~ 0 + Gender, data = Galton)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.2288 -1.6102 -0.1102  1.7712  9.7712 
## 
## Coefficients:
##         Estimate Std. Error t value Pr(>|t|)    
## GenderF  64.1102     0.1206   531.7   <2e-16 ***
## GenderM  69.2288     0.1164   595.0   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.509 on 896 degrees of freedom
## Multiple R-squared:  0.9986, Adjusted R-squared:  0.9986 
## F-statistic: 3.184e+05 on 2 and 896 DF,  p-value: < 2.2e-16

summary(mixedmod)

## Linear mixed model fit by REML ['lmerMod']
## Formula: Height ~ 0 + Gender + (1 | FamilyID)
##    Data: Galton
## 
## REML criterion at convergence: 4007.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.9475 -0.5661  0.0067  0.5937  3.5069 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  FamilyID (Intercept) 2.448    1.564   
##  Residual             3.843    1.960   
## Number of obs: 898, groups:  FamilyID, 197
## 
## Fixed effects:
##         Estimate Std. Error t value
## GenderF  64.1489     0.1542   415.9
## GenderM  69.3019     0.1505   460.5
## 
## Correlation of Fixed Effects:
##         GendrF
## GenderM 0.567

The mixed model has larger standard errors. This makes sense because of sample size.

10. The variance of the error not captured by the gender factor and created by the random family ID effect.

11. The variance in the height factors of family IDs. Between group variance.

12. Negative

13. Negative

Note: Most of this is from Cheyanne