```
library(FSA) ## for peek(), vbFuns(), vbStarts(), SpotVA1
library(dplyr) ## for mutate()
library(ggplot2)
library(patchwork) ## placing plots (in conclusion)
theme_set(theme_bw())
```

# Introduction

We deprecated `residPlot()`

from FSA v0.9.0 and fully removed it by the start of 2022. We took this action to make `FSA`

more focused on fisheries applications and to eliminate “black box” functions. `residPlot()`

was originally designed for students to quickly visualize residuals from one- and two-way ANOVAs and simple, indicator variable, and logistic regressions.^{1} We now feel that students are better served by learning how to create these visualizations using methods provided by `ggplot2`

, which require more code, but are more modern, flexible, and transparent.

^{1} Over time functionality for non-linear regressions was added.

The basic plots produced by `residPlot()`

are recreated here using `ggplot2`

to provide a resource to help users that relied on `residPlot()`

transition to `ggplot2`

.

# Example Data

Most examples below use the `Mirex`

data set from `FSA`

, which contains the concentration of mirex in the tissue and the body weight of two species of salmon (`chinook`

and `coho`

) captured in six years. The `year`

variable is converted to a factor for modeling purposes and a new variable is created that indicates if the mirex concentration was greater that 0.2 or not. These same data were used in this post about removing `fitPlot()`

from `FSA`

.^{2}

^{2} `peek()`

from `FSA`

is used to examine a portion of the data from evenly-spaced row.

```
data(Mirex,package="FSA")
<- Mirex |>
Mirex mutate(year=factor(year),
gt2=ifelse(mirex>0.2,1,0))
peek(Mirex,n=10)
```

```
#R| year weight mirex species gt2
#R| 1 1977 0.41 0.16 chinook 0
#R| 14 1977 3.29 0.23 coho 1
#R| 27 1982 0.70 0.10 coho 0
#R| 41 1982 5.09 0.27 coho 1
#R| 54 1986 1.82 0.12 chinook 0
#R| 68 1986 8.40 0.13 chinook 0
#R| 81 1992 10.00 0.48 chinook 1
#R| 95 1996 5.70 0.16 coho 0
#R| 108 1999 5.11 0.11 coho 0
#R| 122 1999 11.82 0.09 chinook 0
```

# One-Way ANOVA

The code below fits a one-way ANOVA model to examine if mean weight differs by species.

```
<- lm(weight~species,data=Mirex)
aov1 anova(aov1)
```

```
#R| Analysis of Variance Table
#R|
#R| Response: weight
#R| Df Sum Sq Mean Sq F value Pr(>F)
#R| species 1 282.4 282.399 27.657 6.404e-07 ***
#R| Residuals 120 1225.3 10.211
#R| ---
#R| Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

`residPlot()`

from `FSA`

produced a boxplot of residuals by group (left) and a histogram of residuals (right).

`::residPlot(aov1) FSAmisc`

A data frame of the two variables used in the ANOVA appended with the fitted values and residuals from the model fit must be made to construct this plot using `ggplot()`

. Studentized residuals are included below in case you would prefer to plot them.^{3}

^{3} These are “internally” Studentized residuals. “Externally” Studentized residuals can be obtained with `rstandard()`

.

```
<- Mirex |>
tmp select(weight,species) |>
mutate(fits=fitted(aov1),
resids=resid(aov1),
sresids=rstudent(aov1))
peek(tmp,n=8)
```

```
#R| weight species fits resids sresids
#R| 1 0.41 chinook 6.314776 -5.9047761 -1.8814369
#R| 17 4.77 coho 3.257091 1.5129091 0.4762846
#R| 35 2.92 chinook 6.314776 -3.3947761 -1.0710643
#R| 52 1.70 coho 3.257091 -1.5570909 -0.4902213
#R| 70 9.53 chinook 6.314776 3.2152239 1.0139117
#R| 87 0.90 coho 3.257091 -2.3570909 -0.7430562
#R| 105 2.61 coho 3.257091 -0.6470909 -0.2035546
#R| 122 11.82 chinook 6.314776 5.5052239 1.7507263
```

The histogram of residuals is constructed with `geom_histogram()`

below. Note that the color of the histogram bars are modified and the bin width is set to better control the number of bars in the histogram. Finally, the bottom multiplier for the y-axis is set to zero so that that histogram bars do not “hover” above the x-axis.

```
ggplot(data=tmp,mapping=aes(x=resids)) +
geom_histogram(color="gray30",fill="gray70",binwidth=0.5) +
scale_y_continuous(expand=expansion(mult=c(0,0.05)))
```

The boxplot of residuals by group (species in this case) is constructed with `geom_boxplot()`

below (again controlling the colors of the boxplot).

```
ggplot(data=tmp,mapping=aes(x=species,y=resids)) +
geom_boxplot(color="gray30",fill="gray70")
```

These plots can be further modified using methods typical for ggplot (see conclusion section).

# Two-Way ANOVA

The code below fits a two-way ANOVA model to examine if mean weight differs by species, by year, or by the interaction between species and year.

```
<- lm(weight~year*species,data=Mirex)
aov2 anova(aov2)
```

```
#R| Analysis of Variance Table
#R|
#R| Response: weight
#R| Df Sum Sq Mean Sq F value Pr(>F)
#R| year 5 281.86 56.373 6.9954 1.039e-05 ***
#R| species 1 221.69 221.689 27.5099 7.648e-07 ***
#R| year:species 5 117.69 23.538 2.9208 0.01628 *
#R| Residuals 110 886.44 8.059
#R| ---
#R| Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

`residPlot()`

from `FSA`

showed a boxplot of residuals by each combination of the two factor variables (left) and a histogram of the residuals (right).

`::residPlot(aov2) FSAmisc`

A data frame of the three variables used in the ANOVA appended with the fitted values and residuals from the model fit must be constructed.

```
<- Mirex |>
tmp select(weight,species,year) |>
mutate(fits=fitted(aov2),
resids=resid(aov2),
sresids=rstudent(aov2))
```

The histogram of residuals is constructed exactly as before and won’t be repeated here. The boxplot of residuals by group is constructed with one of the factor variables on the x-axis and the other factor variable as separate facets.^{4}

^{4} These two variables can, of course, be exchanged. However, I generally prefer to have the variable with more levels on the x-axis.

```
ggplot(data=tmp,mapping=aes(x=year,y=resids)) +
geom_boxplot(color="gray30",fill="gray70") +
facet_wrap(vars(species))
```

# Simple Linear Regression

The code below fits a simple linear regression for examining the relationship between mirex concentration and salmon weight.

```
<- lm(mirex~weight,data=Mirex)
slr anova(slr)
```

```
#R| Analysis of Variance Table
#R|
#R| Response: mirex
#R| Df Sum Sq Mean Sq F value Pr(>F)
#R| weight 1 0.22298 0.222980 26.556 1.019e-06 ***
#R| Residuals 120 1.00758 0.008396
#R| ---
#R| Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

`residPlot()`

from `FSA`

showed a scatterplot of residuals versus fitted values (left) and a histogram of residuals (right).

`::residPlot(slr) FSAmisc`

A data frame of the two variables used in the ANOVA appended with the fitted values and residuals from the model fit must be constructed.

```
<- Mirex |>
tmp select(weight,mirex) |>
mutate(fits=fitted(slr),
resids=resid(slr),
sresids=rstudent(slr))
```

The histogram of residuals is constructed exactly as before and won’t be repeated here. The scatterplot of residuals versus fitted values is constructed with `geom_point()`

as below. Note that `geom_hline()`

is used to place the horizontal line at 0 on the y-axis.

```
ggplot(data=tmp,mapping=aes(x=fits,y=resids)) +
geom_point() +
geom_hline(yintercept=0,linetype="dashed")
```

It is also possible to include a loess smoother to help identify a possible nonlinearity in this residual plot.

```
ggplot(data=tmp,mapping=aes(x=fits,y=resids)) +
geom_point() +
geom_hline(yintercept=0,linetype="dashed") +
geom_smooth()
```

# Indicator Variable Regression

The code below fits an indicator variable regression to examine if the relationship between mirex concentration and salmon weight differs betwen species.

```
<- lm(mirex~weight*species,data=Mirex)
ivr anova(ivr)
```

```
#R| Analysis of Variance Table
#R|
#R| Response: mirex
#R| Df Sum Sq Mean Sq F value Pr(>F)
#R| weight 1 0.22298 0.222980 26.8586 9.155e-07 ***
#R| species 1 0.00050 0.000498 0.0600 0.80690
#R| weight:species 1 0.02744 0.027444 3.3057 0.07158 .
#R| Residuals 118 0.97964 0.008302
#R| ---
#R| Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

`residPlot()`

from `FSA`

is the same for an IVR as for an SLR, except that the points on the residual plot (left) had different colors for the different groups.

`::residPlot(ivr) FSAmisc`

A data frame of the three variables used in the ANOVA appended with the fitted values and residuals from the model fit must be constructed.

```
<- Mirex |>
tmp select(weight,mirex,species) |>
mutate(fits=fitted(ivr),
resids=resid(ivr),
sresids=rstudent(ivr))
```

The histogram of residuals is constructed exactly as before and won’t be repeated here. The scatterplot of residuals versus fitted values is constructed with `geom_point()`

. Note that `color=`

and `shape=`

are both set equal to the factor variable to change the color and plotting character to represent the different groups.

```
ggplot(data=tmp,mapping=aes(x=fits,y=resids,color=species,shape=species)) +
geom_point() +
geom_hline(yintercept=0,linetype="dashed")
```

# Nonlinear Regression

The following code fits a von Bertalanffy growth function (VBGF) to the total length and age data for spot found in the `SpotVA1`

data frame built into `FSA`

. Fitting the VBGF is described in more detail here.

```
<- vbFuns()
vb <- vbStarts(tl~age,data=SpotVA1)
vbs <- nls(tl~vb(age,Linf,K,t0),data=SpotVA1,start=vbs) nlreg
```

`residPlot()`

from `FSA`

produced plots exactly as for a simple linear regression.

`::residPlot(nlreg) FSAmisc`

A data frame of the two variables used in the ANOVA appended with the fitted values and residuals from the model fit must be constructed. The `rstudent()`

function does not work for non-linear models, but the Studentized residuals are computed with `nlsResiduals()`

from `nlstools`

. However, these values are “buried” in the `Standardized residuals`

column of the `resi2`

matrix returned by that function; thus, it takes a little work to extract them as shown below.

```
<- SpotVA1 |>
tmp select(tl,age) |>
mutate(fits=fitted(nlreg),
resids=resid(nlreg),
sresids=nlstools::nlsResiduals(nlreg)$resi2[,"Standardized residuals"])
peek(tmp,n=8)
```

```
#R| tl age fits resids sresids
#R| 1 6.5 0 7.348034 -0.8480343 -0.8051925
#R| 58 8.3 1 9.251581 -0.9515812 -0.9035082
#R| 115 8.5 1 9.251581 -0.7515812 -0.7136121
#R| 173 9.7 1 9.251581 0.4484188 0.4257650
#R| 230 9.8 2 10.771696 -0.9716957 -0.9226066
#R| 288 10.5 2 10.771696 -0.2716957 -0.2579700
#R| 345 11.5 3 11.985613 -0.4856128 -0.4610802
#R| 403 13.9 4 12.955010 0.9449900 0.8972498
```

Once this data frame is constructed the residual plot and histogram of residuals are constructed exactly as for linear regression and won’t be repeated here.

# Conclusion

The `residPlot()`

function in `FSA`

was removed by 2022. This post describes a more transparent (i.e., not a “black box”) and flexible set of methods for constructing similar plots using `ggplot2`

for those who will need to transition away from using `residPlot()`

.^{5}

^{5} Different “residual plots” are available in `plot()`

(from base R when given an object from `lm()`

), `car::residualPlots()`

, `DHARMa::plotResiduals()`

, and `ggResidpanel::resid_panel()`

.

As mentioned in the examples above, each plot can be modified further using typical methods for `ggplot2`

. These changes were not illustrated above to minimize the amount of code shown in this post. However, as an example, the code below shows a possible modification of the IVR residual plot shown above.^{6}

^{6} `patchwork`

is used here to place the plots side-by-side.

```
## Recreate the data frame of results for the IVR
<- Mirex |>
tmp select(weight,mirex,species) |>
mutate(fits=fitted(ivr),
resids=resid(ivr),
sresids=rstudent(ivr))
## Create a general theme that can be applied to both plots
<- theme_bw() +
theme_DHO theme(panel.grid.major=element_line(color="gray90",linetype="dashed"),
panel.grid.minor=element_blank(),
axis.title=element_text(size=rel(1.25)),
axis.text=element_text(size=rel(1.1)),
legend.position=c(0,1),
legend.justification=c(-0.05,1.02),
legend.title=element_blank(),
legend.text=element_text(size=rel(1.1)))
## Construct the residual plot
<- ggplot(tmp,aes(x=fits,y=sresids,color=species)) +
r1 geom_point(size=1.5,alpha=0.5) +
geom_hline(yintercept=0,linetype="dashed") +
geom_smooth(se=FALSE) +
scale_y_continuous(name="Studentized Residuals") +
scale_x_continuous(name="Fitted Values") +
scale_color_manual(values=c("#E69F00","#0072B2"),guide="none") +
theme_DHO
## Construct the histogram of residuals
<- ggplot(tmp,aes(x=sresids,color=species,fill=species)) +
r2 geom_histogram(alpha=0.5,binwidth=0.25) +
scale_y_continuous(name="Frequency",expand=expansion(mult=c(0,0.05))) +
scale_x_continuous(name="Studentized Residuals") +
scale_color_manual(values=c("#E69F00","#0072B2"),
aesthetics=c("color","fill")) +
theme_DHO
## Put plots side-by-side (the "+" is provided by patchwork)
+ r2 r1
```

## Reuse

## Citation

```
@online{h.ogle2021,
author = {Derek H. Ogle},
title = {Replace {residPlot()} with Ggplot},
date = {2021-06-01},
url = {https://fishr-core-team.github.io/fishR//blog/posts/2021-6-1_residPlot-replacement},
langid = {en}
}
```