The `mosaicModel`

package aims to make it easier to display, compare, and interpret a wide range of statistical models, including the standards such as `lm`

and `glm`

, as well as “machine learning” architectures such as tree-based models (e.g. `randomForest`

), k-nearest neighbors, linear and discriminant analysis, etc.

Install the CRAN version of `mosaicModel`

in the usual way.

Updates, bug fixes, etc. not yet available on CRAN are posted through this repository on github. You can install `mosaicModel`

from github with:

```
# install.packages("devtools")
devtools::install_github("ProjectMOSAIC/mosaicModel")
```

One goal of `mosaicModel`

is to facilitate teaching statistics in a modern, model-based way. Part of this is being able to introduce covariates early. To illustrate, consider scores on the SAT college-admission test broken down by state. The question is whether higher per-pupil spending is associated with higher test scores. (This is one of the examples in the 2017 GAISE College Report.)

```
data(SAT, package = "mosaicData")
mod1 <- lm(sat ~ ns(expend, 2), data = SAT)
mod_plot(mod1, interval = "confidence") %>%
gf_point(sat ~ expend, data = SAT, alpha = 0.5)
```

A pretty convicing downward trend in the regression curve. The confidence band suggests, though, that this might be an accidental pattern. This possibility can be confirmed more formally by looking at the “effect size,” how a change in the input `expend`

in the model corresponds to a change in output from the model. (Whether `expend`

is causal or not in the real world is another issue, but it’s certainly “causal” in the model!)

```
mod_effect(mod1, ~ expend, expend = 5, bootstrap = 50)
#> # A tibble: 1 x 4
#> slope_mean slope_se expend to_expend
#> <dbl> <dbl> <dbl> <dbl>
#> 1 -26.1 8.67 5 6
```

OK, no strong evidence that expenditure has an impact on SAT scores.

It turns out that at the time the `SAT`

data were collected, states differed markedly in the fraction of high-school students who take the test. The `frac`

is a covariate: a variable in which we are not directly interested but which might play an important role in the system overall.

```
data(SAT, package = "mosaicData")
mod2 <- lm(sat ~ ns(expend, 2) * frac, data = SAT)
mod_plot(mod2, interval = "confidence")
```

```
mod_effect(mod2, ~ expend, expend = 5, frac = c(10,50,90), bootstrap = 50)
#> # A tibble: 3 x 5
#> slope_mean slope_se expend to_expend frac
#> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 4.09 9.44 5 6 10
#> 2 39.4 7.56 5 6 50
#> 3 74.8 16.7 5 6 90
```

A much more nuanced effect. For states where few students take the SAT, there is little or no dependence of scores on expenditure. Incidently, those states tend to have very high SAT scores compared to others. The usual explanation of this is that in such states only the very best students, often those bound for out-of-state universities, take the SAT.

Among states with low expenditures, there’s notable increase in score performance as expenditure increases.

This example shows the display of a classifier model of `Species`

on the famous `iris`

data.

```
species_mod <- qda(Species ~ Petal.Length + Petal.Width, data = iris)
mod_plot(species_mod, bootstrap = 10, class_level = "virginica") %>%
gf_theme(legend.position = "top")
```

That’s a crazy complicated graph for an introductory example, but stick with me. The graph shows the classification probability generated by the model that an iris of a given petal width and petal length is species *virginica*.

- For petals of width 3 (blue line), regardless of the petal length, the classification probability is essentially 100%.
- For petals of width 1 and length between 3 and 4, the classification probability is zero.
- For petals slightly longer than four or less than two, bootstrapped replicates (the several red curves) vary a lot, suggesting that the
`iris`

data do not pin down the model very well.