ENVX2001 - Model selection

Learning Outcomes

In this lab, you will work towards achieving learning outcomes

Lab Objectives

In this lab, we will:

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Tip

Please work on this exercise by creating your own R Markdown file.

Exercise 1: Model quality - multiple vs adjusted r2

Data: California_streamflow spreadsheet

Import the “California_streamflow” sheet into R.

# Load library if needed
library(readxl)
# Load data
stream_data <- read_xlsx("data/california_streamflow.xlsx", "streamflow")

in this exercise we will use the same data as last week. To jog your memory, the dataset contains 43 years of annual precipitation measurements (in mm) taken at (originally) 6 sites in the Owens Valley in California. Through model selection via partial F-test we have the final model as below:

fit <- lm(runoff_volume ~ rock_creek + pine_creek, data = stream_data)

We will now add a totally useless variable to the dataset. This variable is a random number generated from a normal distribution with mean 3 and standard deviation 2. We use the set.seed() function to make sure that everybody gets the same random values.

set.seed(100) # to make sure everybody gets the same results

# this generates the random number into the dataset
stream_data$random_no <- rnorm(n = nrow(stream_data), mean = 3, sd = 2)

We will see the impact of including a totally useless variable, such as this random variable, has on measures of model quality, r2 and adjusted r2 values.

Task: create two regression models:

  1. runoff_volume ~ rock_creek + pine_creek
  2. runoff_volume ~ rock_creek + pine_creek + random_no

Question 2

Compare each in terms of their multiple r2 and adjusted r2 values. Which performance measure (multiple r2 or adj r2) would you use to identify which predictors to use in your model?

Exercise 2: Fish productivity

Fish communities were surveyed in lakes across a eutrophication gradient to investigate the relatioship between productivity and fish diversity.

The datasheet has thefollowing variables:

  • lake_id Unique identifier for each lake
  • chla Log-transformed Chlorophyll a
  • richness Log-transformed species richness
  • evenness Log-transformed Pielou’s evenness
  • abundance Log-transformed abundance per unit effort (NPUE)
  • biomass Log-transformed biomass per unit effort (BPUE)
  • productivity Log-transformed productivity proxy
#Load library if necessary
library(tidyverse)

#Read in data
fish_data <- read_csv("data/fish_communities.csv")
Rows: 39 Columns: 7
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (1): lake_id
dbl (6): chla, richness, evenness, abundance, biomass, productivity

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
#Have a look at the structure of the data
str(fish_data)
spc_tbl_ [39 × 7] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
 $ lake_id     : chr [1:39] "FTH" "XLH" "HGH" "LH" ...
 $ chla        : num [1:39] 4.61 4.53 3.84 3.71 2.43 ...
 $ richness    : num [1:39] 2.64 2.89 1.99 2.94 2.37 ...
 $ evenness    : num [1:39] -0.356 -0.67 -0.423 -0.405 -0.589 ...
 $ abundance   : num [1:39] 2.24 3.34 1.24 2.67 1.12 ...
 $ biomass     : num [1:39] 4.96 6.03 4.67 6.52 5.32 ...
 $ productivity: num [1:39] 3.47 4.47 2.71 4.47 3.24 ...
 - attr(*, "spec")=
  .. cols(
  ..   lake_id = col_character(),
  ..   chla = col_double(),
  ..   richness = col_double(),
  ..   evenness = col_double(),
  ..   abundance = col_double(),
  ..   biomass = col_double(),
  ..   productivity = col_double()
  .. )
 - attr(*, "problems")=<externalptr>

Explore the data on your own before making any models. (Hint: remember that we are only interested in the numeric variables for our linear models)

Question 1

Are there any obvious relationships between the response variable (productivity) and the other variables?

Question 2

Are there any other patterns or potential issues you can see from the exploratory plots?

Take home exercise:

Review

Attribution