February 26, 2019

Types of variables

Week 1

Welcome to SCIE807 Advanced Ecological Data Analysis

What to expect from this course?  

  • Exponential increase in stats and R skills
  • Coding till your eyes are bleeding ;-)
Week 1

Linear models and their specifications

Week 1

Linear models and their specifications

Analysis of variance and linear regression are closely related linear models and can both be specified with the same function (lm) using a formula notation. This approach uses the '~' symbol (tilde), which reads 'as a function of' and connects the left hand side (LHS) of the formula with the right hand side (RHS), i.e. it links the response variable to the explanatory variable(s).

lm(y ~ x, data = ...)

lm(y ~ x1 + x2, data = ...)
Week 1

Linear models and their specifications

Interactive effects of the explantory variables on the predictor, so-called interactions are specified using the colon ':'. To save ourselves some coding, we can simply use the shorthand asterisk '*' notation to include all main effects and interactions. 

lm(y ~ x1 + x2 + x1:x2, data = ...)

## Can be written as:
lm(y ~ x1 * x2, data = ...)

## ...even with more than two explanatory variables
lm(y ~ x1 * x2 * x3, data = ...)
Week 1

The principle of test statistics

A test statistic (t-value, F-value, …) can be regarded a signal-to-noise ratio. The higher the ratio, the easier it becomes to detect a true signal. E.g. the t-statistic of a t-test boils down to the difference in group means (signal) divided by the pooled standard error (noise).
Week 1

Analysis of variance (ANOVA)

## Using the built-in data set PlantGrowth
data(PlantGrowth)
str(PlantGrowth)
## 'data.frame':    30 obs. of  2 variables:
##  $ weight: num  4.17 5.58 5.18 6.11 4.5 4.61 5.17 4.53 5.33 5.14 ...
##  $ group : Factor w/ 3 levels "ctrl","trt1",..: 1 1 1 1 1 1 1 1 1 1 ...
summary(PlantGrowth)
##      weight       group   
##  Min.   :3.590   ctrl:10  
##  1st Qu.:4.550   trt1:10  
##  Median :5.155   trt2:10  
##  Mean   :5.073            
##  3rd Qu.:5.530            
##  Max.   :6.310
Week 1

Analysis of variance (ANOVA)

Always carry out sanity checks (str, summary) and plot your data before you get carried away with statistical modelling. What do you conclude looking at the boxplot below?
Week 1