Confirmatory model selection

Instructions:

This html will give you the code and steps to do confirmatory model selection
Data will be named YourData and models YourModel - you should change these to the name you decide to give your data and models

The variable names are also different here as examples are on different data to what you have. Results will also be different

The first step in confirmatory model selection is to work out what your H0 (null hypothesis) and H1 (alternative hypothesis) are.

Once you have worked this out you should run a linear model for each of these. You should know the code to do this by now. Make sure to save them as objects e.g. YourModelH0 <- lm(), because you will use them in other functions later.

Now you have your two models for H0 and H1, use the anova() function to compare them.

anova(YourModel1, YourModel2)

## Analysis of Variance Table
## 
## Model 1: height ~ 1
## Model 2: height ~ type
##   Res.Df    RSS Df Sum of Sq      F  Pr(>F)  
## 1     29 293.44                              
## 2     28 242.08  1    51.352 5.9395 0.02141 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Hint: check the degrees of freedom to see if you put them in the right order. The degrees of freedom should make sense

Now you need to interpret the output. Below is an example from a different dataset.

Degrees of freedom HERE begins as: n (number of data points). But usually n-1

The columns are:

Res.DF - residual degrees of freedom, those left after number of parameters estimated has been removed (here, we have estimated an intercept in both (n-1), and a slope too in one of our models (n-2))
RSS - residual sum of squares. Sum of squared distances between estimate and data points. Estimate can be a mean or a regression line depending on the model.
DF - difference in degrees of freedom between the two models.
Sum of Sq - the RSS of the H0 model - RSS of the H1 model.
F - F statistic. Calculated as (Sum of Sq/df)/(RSS of H1/DF H1). Here that is (51.352/1)/(242.08/28)
Pr(>F) - the probability of getting the F value you have or higher IF H0 were true.

anova(YourModel1, YourModel2)

## Analysis of Variance Table
## 
## Model 1: height ~ 1
## Model 2: height ~ type
##   Res.Df    RSS Df Sum of Sq      F  Pr(>F)  
## 1     29 293.44                              
## 2     28 242.08  1    51.352 5.9395 0.02141 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1