1. As in previous exercises, either create a new R script (perhaps
call it ‘linear_model_2’) or continue with your previous R script in
your RStudio Project. Again, make sure you include any metadata you feel
is appropriate (title, description of task, date of creation etc) and
don’t forget to comment out your metadata with a # at the
beginning of the line.
2. Once again import the data file ‘loyn.txt’ into R and take a look
at the structure of this dataframe using the str()
function. In this exercise you will investigate whether the abundance of
birds (ABUND) is different in areas with different grazing
intensities (GRAZE). Remember, the GRAZE
variable is an index of livestock grazing intensity. Level 1 = low
grazing intensity and level 5 = high grazing intensity.
3. As we discussed in the graphical data exploration exercise the
GRAZE variable was originally coded as a numeric (i.e. 1,
2, 3, 4, 5). In this exercise we actually want to treat
GRAZE as a categorical variable with five levels (aka a
factor). So the first thing we need to do is create a new variable in
the loyn dataframe called FGRAZE in which we
store the GRAZE variable coerced to be a categorical
variable with the factor() function (you can also use the
as.factor() function if you prefer).
4. Explore any potential differences in bird abundance between each
level of FGRAZE graphically using an appropriate plot
(hint: a boxplot might be useful here). How would you interpret this
plot? What might you expect to see in your analysis? Write your
predictions in your R script as a comment. What is the mean number of
birds for each level of FGRAZE?
5. Fit an appropriate linear model in R to explain the variation in
the response variable, ABUND, with the explanatory variable
FGRAZE. Remember to use the data = argument.
Assign this linear model to an appropriately named object
(birds_lm if your imagination fails you!).
6. Produce the ANOVA table using the anova() function on
the model object. What null hypothesis is being tested? Do you reject or
fail to reject the null hypothesis? What summary statistics would you
report? Summarise in your R script as a comment.
7. Use the summary() function on the model object to
produce the table of parameter estimates (remember these are called
coefficients in R). Using this output what is the estimate of the
intercept and what does this represent? What is the null hypothesis
associated with the intercept? do you reject or fail to reject this
hypothesis?
Next we move onto the the FGRAZE2 parameter, how do you
interpret this parameter? (remember they are contrasts). Again, what is
the null hypothesis associated with the FGRAZE2 parameter?
do you reject or fail to reject this hypothesis?
Repeat this interpretation for the FGRAZE3,
FGRAZE4 and FGRAZE5 parameters. Summarise this
as a comment in your R script.
8. Now that you have interpreted all the contrasts with
FGRAZE level 1 as the intercept, set the intercept to
FGRAZE level 2 using the relevel() function,
refit the model, produce the new table of parameter estimates using the
summary() function again and interpret.
Repeat this for FGRAZE levels 3, 4 and 5. Can you
summarise which levels of FGRAZE are different from each
other?
9. Staying with the summary table of parameter estimates, how much of
the variation in bird abundance does the explanatory variable
FGRAZE explain?
10. Now onto a really important part of the model fitting process.
Let’s check the assumptions of your linear model by creating plots of
the residuals from the model. Remember, you can easily create these
plots by using the plot() function on your model object.
Also remember that if you want to see all plots at once then you should
split your plotting device into 2 rows and 2 columns using the
par() function before you create the plots. Check each of
the assumptions using these plots and report whether your model meets
these assumptions in your R script.
11. This is an optional question and really just for information.
I’ll give you the code in the solutions so don’t overly stress about
this! Use Google (yep, this is OK!) to figure out how to plot your
fitted values and 95% confidence intervals. Try Googling the
gplots package or the effects package.
Alternatively, have a go at using our old trusty
predict() function to calculate the fitted values and
standard errors. Add the fitted values and 95% confidence intervals to a
plot of bird abundance and graze level (to add your upper and lower
confidence intervals will need to use either the segments()
or arrows() function).
Or we can even use the ggplot2 package. Check out the
solutions code if you’re thoroughly confused!
End of the linear model with single categorical explanatory variable exercise