Phase II: Using Our Toolbox

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.title[
# Phase II: Using Our Toolbox
]
.subtitle[
## Module 7: Birds of a Feather
]
.author[
### Dr. Christopher Kenaley
]
.institute[
### Boston College
]
.date[
### 2024/18/11
]

---

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# In class today

```
## Warning: package 'ggplot2' was built under R version 4.2.3
```

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.pull-left[
Today we'll ....

- Consider Linear Mixed-effect Modeling

]

.pull-right[

![](https://upload.wikimedia.org/wikipedia/commons/thumb/1/12/Mixedandfixedeffects.jpg/692px-Mixedandfixedeffects.jpg)
]

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## Congrats!

![](IMG_9780.png)

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## Linear Mixed-effect Modeling

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- Other models assume independence of data
- LME included fixed and random effects
- Often termed repeated measures
- Same model formulae, but
  + `+(1|random_effect)`

]

.pull-right[

``` r
iris %>% group_by(Species) %>% summarise_all(.funs = mean)
```

```
## # A tibble: 3 × 5
##   Species    Sepal.Length Sepal.Width Petal.Length Petal.Width
##   <fct>             <dbl>       <dbl>        <dbl>       <dbl>
## 1 setosa             5.01        3.43         1.46       0.246
## 2 versicolor         5.94        2.77         4.26       1.33 
## 3 virginica          6.59        2.97         5.55       2.03
```
]

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## Linear Mixed-effect Modeling

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How do a determine what fixed and random effects are?

- Depends on the question
  + what is independent?
  + what data are dependent, autocorrelated, linked, etc.?

]

.pull-right[

``` r
iris %>% group_by(Species) %>% summarise_all(.funs = mean)
```

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## Linear Mixed-effect Modeling

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Say our question was, is sepal length different between species?

- Species isn't random, it's part of the question

]

.pull-right[

``` r
fit <- lm(Sepal.Length~Species,iris)

anova(fit)
```

```
## Analysis of Variance Table
## 
## Response: Sepal.Length
##            Df Sum Sq Mean Sq F value    Pr(>F)    
## Species     2 63.212  31.606  119.26 < 2.2e-16 ***
## Residuals 147 38.956   0.265                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

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## Linear Mixed-effect Modeling

.pull-left[

Say our question was, is sepal length a function of petal length?

- Species is now random, it's not part of the question

]

.pull-right[

``` r
fit <- lmer(Sepal.Length~Petal.Length+(1|Species),iris)

library(car)
Anova(fit)
```

```
## Analysis of Deviance Table (Type II Wald chisquare tests)
## 
## Response: Sepal.Length
##               Chisq Df Pr(>Chisq)    
## Petal.Length 193.96  1  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```