Data Visualization

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# Data Visualization
## Working with models
### Andrew Irwin, <a href="mailto:a.irwin@dal.ca" class="email">a.irwin@dal.ca</a>
### Math & Stats, Dalhousie University
### 2021-02-08 (updated: 2021-02-05)

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## Models and visualizations

* Adding regression and smoothing lines to ggplot visualizations

* Describing, fitting, and using models

* Linear regression
  
  * Other regression
  
  * Generalized additive models
  
  * LOESS smooths

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##  Examples

* Linear regression

* Polynomial model

* Quantile regression (fitting line to medians or other quantiles)

* Generalized additive model (piecewise splines)

* LOESS (local linear and quadratic regression)

* Putting multiple smooths on one plot

* Smooths on facetted plots

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###  Start with a basic graph

```r
mpg %>% mutate(city_l100km = 235.214583 / cty) %>%
   ggplot(aes(x =displ, y= city_l100km)) + geom_point() +
   labs(x = "Engine displacement (L)",
        y = "Fuel economy, city (L/100km)") + my_theme
```

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### Add a regression line

```r
p + geom_smooth(method = "lm", formula = y ~ x)
```

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### Add a regression line for each group

```r
p + geom_smooth(aes(color = factor(cyl)), method = "lm", formula = y ~ x)
```

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###  Polynomial regression

```r
p + geom_smooth(method = "lm", formula = y ~ poly(x,2))
```

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### Quantile regression

```r
p + geom_quantile(method = "rqss", formula = y ~ x,
                  quantiles = c(0.1, 0.5, 0.9))
```

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### Generalized additive model

```r
p + geom_smooth(method = "lm", 
                formula = y ~ splines::bs(x, df = 5))
```

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### Generalized additive model

```r
p + geom_smooth(method = "gam", 
                formula = y ~ s(x, bs="cs"))
```

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### LOESS

```r
p + geom_smooth(method = "loess", 
                formula = y ~ x) 
```

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### LOESS

```r
p + geom_smooth(method = "loess", formula = y ~ x,
                span = 0.3) 
```

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### Putting multiple smooths on one plot

```r
p + geom_smooth(aes(color = "Linear"), method = "lm", se=FALSE) +
    geom_smooth(aes(color = "GAM"), method = "gam", se=FALSE) +
    geom_smooth(aes(color = "LOESS"), method = "loess", formula = y ~ x, se=FALSE) +
    labs(color = "Type")
```

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### Smooths on facetted plots

```r
p + geom_smooth(method = "lm", se=FALSE, formula = y ~ x) +
  facet_wrap( ~ class)
```

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### Other customizations

```r
p + geom_smooth(method = "lm", se=TRUE, 
                fullrange = TRUE, level = 0.50) + xlim(1,8)
```

<img src="15-working-with-models_files/figure-html/unnamed-chunk-13-1.png" style="display: block; margin: auto;" />
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### Modelling x as a function of y

```r
p + geom_smooth(method = "loess", formula = y ~ x, orientation = "y")
```

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### Modelling x as a function of y

```r
p + geom_smooth(method = "lm", formula = y ~ x, orientation = "y") +
  geom_smooth(method = "lm", formula = y ~ x, color = "red")
```

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# Summary

* Regression lines (based on a model) and "smooths" (no simple model) can be used to draw attention to patterns in data

* We are using smooths for their visual effect

* Logical reasoning for the lines you draw is important (next lessons)

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# Further reading

* Course notes

* Healy Chapter 6. Work with models.

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## Task

Bonus task for this lesson to practice these functions. Nothing to hand in.