`vignettes/different-specifications.Rmd`

`different-specifications.Rmd`

The function `setup()`

seems rather simple, but it is in
fact very versatile and allows to incorporate (almost) any analytic
choice that one might engage in during data analysis. In this vignette,
I am going to exemplify how this function can be used to create several
analytical choices.

One analytic choice may refer to choosing different independent or dependent variables (e.g., different scales that measure the same construct) or different ways in how these variables are compute (e.g., mean vs. latent measurement, log-transformation, etc).

In most cases, this simply means adding such variables to the data set and provide them as alternative choices in setup.

```
# Setup specs
specs <- setup(data = example_data,
x = c("x1", "x2", "x3", "x4"),
y = c("y1", "y2", "y3"),
model = "lm")
# Summary of specifications
summary(specs, rows = 12)
```

```
## Setup for the Specification Curve Analysis
## -------------------------------------------
## Class: specr.setup -- version: 1.0.1
## Number of specifications: 12
##
## Specifications:
##
## Independent variable: x1, x2, x3, x4
## Dependent variable: y1, y2, y3
## Models: lm
## Covariates: no covariates
## Subsets analyses: all
##
## Function used to extract parameters:
##
## function (x)
## broom::tidy(x, conf.int = TRUE)
## <environment: 0x7f9c37823040>
##
##
## Head of specifications table (first 12 rows):
```

```
## # A tibble: 12 × 6
## x y model controls subsets formula
## <chr> <chr> <chr> <chr> <chr> <glue>
## 1 x1 y1 lm no covariates all y1 ~ x1 + 1
## 2 x1 y2 lm no covariates all y2 ~ x1 + 1
## 3 x1 y3 lm no covariates all y3 ~ x1 + 1
## 4 x2 y1 lm no covariates all y1 ~ x2 + 1
## 5 x2 y2 lm no covariates all y2 ~ x2 + 1
## 6 x2 y3 lm no covariates all y3 ~ x2 + 1
## 7 x3 y1 lm no covariates all y1 ~ x3 + 1
## 8 x3 y2 lm no covariates all y2 ~ x3 + 1
## 9 x3 y3 lm no covariates all y3 ~ x3 + 1
## 10 x4 y1 lm no covariates all y1 ~ x4 + 1
## 11 x4 y2 lm no covariates all y2 ~ x4 + 1
## 12 x4 y3 lm no covariates all y3 ~ x4 + 1
```

```
## # A tibble: 6 × 26
## x y model controls subsets formula model_function term estimate
## <chr> <chr> <chr> <chr> <chr> <glue> <list> <chr> <dbl>
## 1 x1 y1 lm no covariates all y1 ~ x1… <fn> x1 0.620
## 2 x1 y2 lm no covariates all y2 ~ x1… <fn> x1 -0.328
## 3 x1 y3 lm no covariates all y3 ~ x1… <fn> x1 -0.0821
## 4 x2 y1 lm no covariates all y1 ~ x2… <fn> x2 0.272
## 5 x2 y2 lm no covariates all y2 ~ x2… <fn> x2 -0.102
## 6 x2 y3 lm no covariates all y3 ~ x2… <fn> x2 -0.0735
## # ℹ 17 more variables: std.error <dbl>, statistic <dbl>, p.value <dbl>,
## # conf.low <dbl>, conf.high <dbl>, fit_r.squared <dbl>,
## # fit_adj.r.squared <dbl>, fit_sigma <dbl>, fit_statistic <dbl>,
## # fit_p.value <dbl>, fit_df <dbl>, fit_logLik <dbl>, fit_AIC <dbl>,
## # fit_BIC <dbl>, fit_deviance <dbl>, fit_df.residual <int>, fit_nobs <int>
```

However, in some cases, we may have different type of variables
(e.g., a mean vs. a dichotomous variable). In some cases, for example
when this refers to a dependent variable, such a choice of variables
requires also different model estimation functions. So in our setup, we
want to acknowledge for specific variable/model combinations. In the
following, let’s imagine that next to our standard dependent variables
(`y1`

-`y3`

), we also have a dichotomous item
(`y_dich`

; here only recoded from `y1`

). In this
case, we want to specify and add a custom function - here a logistic
model (`glm(formula, data, family = binomial()`

)) - to the
setup.

```
# Dichotomous dependent variable
data <- example_data %>%
mutate(y_dich = ifelse(y1 > mean(y1), 1, 0))
# Specific function
log_glm <- function(formula, data) {
glm(formula, data, family = binomial())
}
# Setup specs
specs <- setup(data = data,
x = c("x1", "x2"),
y = c("y1", "y2", "y3", "y_dich"),
model = c("lm", "log_glm"))
# Check
specs %>%
as_tibble
```

```
## # A tibble: 16 × 7
## x y model controls subsets formula model_function
## <chr> <chr> <chr> <chr> <chr> <glue> <list>
## 1 x1 y1 lm no covariates all y1 ~ x1 + 1 <fn>
## 2 x1 y1 log_glm no covariates all y1 ~ x1 + 1 <fn>
## 3 x1 y2 lm no covariates all y2 ~ x1 + 1 <fn>
## 4 x1 y2 log_glm no covariates all y2 ~ x1 + 1 <fn>
## 5 x1 y3 lm no covariates all y3 ~ x1 + 1 <fn>
## 6 x1 y3 log_glm no covariates all y3 ~ x1 + 1 <fn>
## 7 x1 y_dich lm no covariates all y_dich ~ x1 + 1 <fn>
## 8 x1 y_dich log_glm no covariates all y_dich ~ x1 + 1 <fn>
## 9 x2 y1 lm no covariates all y1 ~ x2 + 1 <fn>
## 10 x2 y1 log_glm no covariates all y1 ~ x2 + 1 <fn>
## 11 x2 y2 lm no covariates all y2 ~ x2 + 1 <fn>
## 12 x2 y2 log_glm no covariates all y2 ~ x2 + 1 <fn>
## 13 x2 y3 lm no covariates all y3 ~ x2 + 1 <fn>
## 14 x2 y3 log_glm no covariates all y3 ~ x2 + 1 <fn>
## 15 x2 y_dich lm no covariates all y_dich ~ x2 + 1 <fn>
## 16 x2 y_dich log_glm no covariates all y_dich ~ x2 + 1 <fn>
```

As we can see, the `setup()`

function produces all
combinations between the variables and the model functions. This is not
meaningful as the logistic model should only be used if the dependent
variable is `y_dich`

. In comparison to specr version 0.2.1,
this is were the strength of version 1.0.0 comes in. Because we setup
all specifications beforehand, we can simply remove those that we are
not interested in or that we deem non-meaningful. Note: You won’t be
able to filter or subset the `specr.setup`

object
(essentially a list). Instead, you want to filter/subset the first
position of the list: the data frame that includes the specifications
(here `specs$specs`

or `specs[[1]]`

).

```
# Filter out models that are not meaningful (here only keep log_glm, when y == "y4")
specs$specs <- specs$specs %>%
filter(!(model == "log_glm" & y != "y_dich")) %>%
filter(!(model == "lm" & y == "y_dich"))
# Check results (only meaningful specifications remain)
summary(specs, rows = 8)
```

```
## Setup for the Specification Curve Analysis
## -------------------------------------------
## Class: specr.setup -- version: 1.0.1
## Number of specifications: 16
##
## Specifications:
##
## Independent variable: x1, x2
## Dependent variable: y1, y2, y3, y_dich
## Models: lm, log_glm
## Covariates: no covariates
## Subsets analyses: all
##
## Function used to extract parameters:
##
## function (x)
## broom::tidy(x, conf.int = TRUE)
## <environment: 0x7f9c32e50ba8>
##
##
## Head of specifications table (first 8 rows):
```

```
## # A tibble: 8 × 6
## x y model controls subsets formula
## <chr> <chr> <chr> <chr> <chr> <glue>
## 1 x1 y1 lm no covariates all y1 ~ x1 + 1
## 2 x1 y2 lm no covariates all y2 ~ x1 + 1
## 3 x1 y3 lm no covariates all y3 ~ x1 + 1
## 4 x1 y_dich log_glm no covariates all y_dich ~ x1 + 1
## 5 x2 y1 lm no covariates all y1 ~ x2 + 1
## 6 x2 y2 lm no covariates all y2 ~ x2 + 1
## 7 x2 y3 lm no covariates all y3 ~ x2 + 1
## 8 x2 y_dich log_glm no covariates all y_dich ~ x2 + 1
```

```
## # A tibble: 6 × 28
## x y model controls subsets formula model_function term estimate
## <chr> <chr> <chr> <chr> <chr> <glue> <list> <chr> <dbl>
## 1 x1 y1 lm no covaria… all y1 ~ x… <fn> x1 0.620
## 2 x1 y2 lm no covaria… all y2 ~ x… <fn> x1 -0.328
## 3 x1 y3 lm no covaria… all y3 ~ x… <fn> x1 -0.0821
## 4 x1 y_dich log_glm no covaria… all y_dich… <fn> x1 0.753
## 5 x2 y1 lm no covaria… all y1 ~ x… <fn> x2 0.272
## 6 x2 y2 lm no covaria… all y2 ~ x… <fn> x2 -0.102
## # ℹ 19 more variables: std.error <dbl>, statistic <dbl>, p.value <dbl>,
## # conf.low <dbl>, conf.high <dbl>, fit_r.squared <dbl>,
## # fit_adj.r.squared <dbl>, fit_sigma <dbl>, fit_statistic <dbl>,
## # fit_p.value <dbl>, fit_df <dbl>, fit_logLik <dbl>, fit_AIC <dbl>,
## # fit_BIC <dbl>, fit_deviance <dbl>, fit_df.residual <int>, fit_nobs <int>,
## # fit_null.deviance <dbl>, fit_df.null <int>
```

In some cases, we may want to add mean indices or even latent
measurement models of our variables of interest to explore how latent
vs. manifest measurement affects our results. This requires a bit more
upfront work as we need to work with lavaan for the latent measurement.
Furthermore, we need to adjust the extract functions (`fun1`

and `fun2`

in `setup()`

) so that the extraction of
parameters aligns across different type of models. The beauty of
`broom::tidy()`

and `broom::glance()`

(which are
used by default) is that they adapt to the different model types that
are passed to `setup`

. Although the same parameters are
extracted for most models, they sometimes differ for specific models
(e.g., structural equation models resulting from
`lavaan::sem()`

). This means we need to adjust them to
extract the same parameters across different models.

```
# Add mean (one choice)
data <- data %>%
rowwise %>%
mutate(x_mean = mean(x1, x2, x3, x4)) %>%
ungroup
# Add custom function with latent measurement models to pass to "models" (another choice)
custom_sem <- function(formula, data) {
# Make sure lavaan is loaded
require(lavaan)
# Add latent measurement as list
latent <- list(latent_x12 = "latent_x12 =~ x1 + x2")
# Remove +1 from formula as lavaan doesn't know how to process it
semformula <- str_remove_all(formula, "\\+ 1")
# remove non-used latent measurement models from list by checking the formula
valid <- purrr::keep(names(latent), ~ stringr::str_detect(formula, .x))
# Create new formula that includes latent measurement models
formula <- paste(formula, "\n", paste(latent[valid], collapse = " \n "))
# Pass formula to `sem()`
sem(formula, data)
}
# Create custom tidy function that extracts the same parameters from different models!
tidy_new <- function(x) {
if(class(x) == "lavaan") {
broom::tidy(x, conf.int = TRUE) %>%
select(term, estimate, conf.low, conf.high) %>% # select parameters you want to keep
filter(grepl(" ~ ", term)) %>% # term needs to be adjusted
separate(term, c("dv", "term"), sep = " ~ ") %>% # extract independent variable
select(-dv) # remove dependent variable
} else {
broom::tidy(x, conf.int = TRUE) %>%
select(term, estimate, conf.low, conf.high) # same parameters as above
}
}
# Setup specs with new custom function
specs <- setup(data = data,
x = c("x1", "x2", "x3", "x4", "x_mean", "latent_x12"),
y = c("y1", "y2"),
model = c("lm", "custom_sem"),
fun1 = tidy_new, # We pass the new extract function
fun2 = NULL) # switch off "glance" as it produces different fit indices and wouldn't work
# Quick check (still includes non-meaningful specifications)
summary(specs, rows = 12)
```

```
## Setup for the Specification Curve Analysis
## -------------------------------------------
## Class: specr.setup -- version: 1.0.1
## Number of specifications: 24
##
## Specifications:
##
## Independent variable: x1, x2, x3, x4, x_mean, latent_x12
## Dependent variable: y1, y2
## Models: lm, custom_sem
## Covariates: no covariates
## Subsets analyses: all
##
## Function used to extract parameters:
##
## function(x) {
## if(class(x) == "lavaan") {
## broom::tidy(x, conf.int = TRUE) %>%
## select(term, estimate, conf.low, conf.high) %>% # select parameters you want to keep
## filter(grepl(" ~ ", term)) %>% # term needs to be adjusted
## separate(term, c("dv", "term"), sep = " ~ ") %>% # extract independent variable
## select(-dv) # remove dependent variable
## } else {
## broom::tidy(x, conf.int = TRUE) %>%
## select(term, estimate, conf.low, conf.high) # same parameters as above
## }
## }
##
##
## Head of specifications table (first 12 rows):
```

```
## # A tibble: 12 × 6
## x y model controls subsets formula
## <chr> <chr> <chr> <chr> <chr> <glue>
## 1 x1 y1 lm no covariates all y1 ~ x1 + 1
## 2 x1 y1 custom_sem no covariates all y1 ~ x1 + 1
## 3 x1 y2 lm no covariates all y2 ~ x1 + 1
## 4 x1 y2 custom_sem no covariates all y2 ~ x1 + 1
## 5 x2 y1 lm no covariates all y1 ~ x2 + 1
## 6 x2 y1 custom_sem no covariates all y1 ~ x2 + 1
## 7 x2 y2 lm no covariates all y2 ~ x2 + 1
## 8 x2 y2 custom_sem no covariates all y2 ~ x2 + 1
## 9 x3 y1 lm no covariates all y1 ~ x3 + 1
## 10 x3 y1 custom_sem no covariates all y1 ~ x3 + 1
## 11 x3 y2 lm no covariates all y2 ~ x3 + 1
## 12 x3 y2 custom_sem no covariates all y2 ~ x3 + 1
```

```
# Filter out non-meaningful specifications
specs$specs <- specs$specs %>%
filter(!(model == "custom_sem" & !grepl("latent", x))) %>%
filter(!(model == "lm" & grepl("latent", x)))
# Check again
summary(specs, rows = 12)
```

```
## Setup for the Specification Curve Analysis
## -------------------------------------------
## Class: specr.setup -- version: 1.0.1
## Number of specifications: 24
##
## Specifications:
##
## Independent variable: x1, x2, x3, x4, x_mean, latent_x12
## Dependent variable: y1, y2
## Models: lm, custom_sem
## Covariates: no covariates
## Subsets analyses: all
##
## Function used to extract parameters:
##
## function(x) {
## if(class(x) == "lavaan") {
## broom::tidy(x, conf.int = TRUE) %>%
## select(term, estimate, conf.low, conf.high) %>% # select parameters you want to keep
## filter(grepl(" ~ ", term)) %>% # term needs to be adjusted
## separate(term, c("dv", "term"), sep = " ~ ") %>% # extract independent variable
## select(-dv) # remove dependent variable
## } else {
## broom::tidy(x, conf.int = TRUE) %>%
## select(term, estimate, conf.low, conf.high) # same parameters as above
## }
## }
##
##
## Head of specifications table (first 12 rows):
```

```
## # A tibble: 12 × 6
## x y model controls subsets formula
## <chr> <chr> <chr> <chr> <chr> <glue>
## 1 x1 y1 lm no covariates all y1 ~ x1 + 1
## 2 x1 y2 lm no covariates all y2 ~ x1 + 1
## 3 x2 y1 lm no covariates all y1 ~ x2 + 1
## 4 x2 y2 lm no covariates all y2 ~ x2 + 1
## 5 x3 y1 lm no covariates all y1 ~ x3 + 1
## 6 x3 y2 lm no covariates all y2 ~ x3 + 1
## 7 x4 y1 lm no covariates all y1 ~ x4 + 1
## 8 x4 y2 lm no covariates all y2 ~ x4 + 1
## 9 x_mean y1 lm no covariates all y1 ~ x_mean + 1
## 10 x_mean y2 lm no covariates all y2 ~ x_mean + 1
## 11 latent_x12 y1 custom_sem no covariates all y1 ~ latent_x12 + 1
## 12 latent_x12 y2 custom_sem no covariates all y2 ~ latent_x12 + 1
```

As we can see, we can now investigate the manifest and latent measures next to the individual items.

Another analytical choice may refer to the inclusion of covariates.
Here, the `setup()`

function is again very versatile and
allows to include different combinations of covariates.

By providing just a vector of covariates, `setup()`

produces all combinations of these covariates plus a specification
without any covariates. If we add the argument
`simplify = TRUE`

, not all combinations between covariates
are created. Instead, only no covariates, each individually, and all
together are included.

```
# Setup specification that include all combinations of covariates
specs1 <- setup(data = example_data,
x = c("x1", "x2"),
y = c("y1", "y2"),
model = "lm",
controls = c("c1", "c2", "c3", "c4")) # simply providing a vector of control variables
# Setup secifications that include only no covariates, each individually, and all together
specs2 <- setup(data = example_data,
x = c("x1", "x2"),
y = c("y1", "y2"),
model = "lm",
controls = c("c1", "c2", "c3", "c4"),
simplify = TRUE) # Difference to specs1!
# Check
distinct(specs1$specs, controls)
```

```
## # A tibble: 16 × 1
## controls
## <chr>
## 1 no covariates
## 2 c1
## 3 c2
## 4 c3
## 5 c4
## 6 c1 + c2
## 7 c1 + c3
## 8 c1 + c4
## 9 c2 + c3
## 10 c2 + c4
## 11 c3 + c4
## 12 c1 + c2 + c3
## 13 c1 + c2 + c4
## 14 c1 + c3 + c4
## 15 c2 + c3 + c4
## 16 c1 + c2 + c3 + c4
```

`distinct(specs2$specs, controls)`

```
## # A tibble: 6 × 1
## controls
## <chr>
## 1 no covariates
## 2 c1
## 3 c2
## 4 c3
## 5 c4
## 6 all covariates
```

We can also add groups of covariates. The way setup creates combinations between such groups remains the same.

```
# Add groups of covariates
specs3 <- setup(data = example_data,
x = c("x1", "x2"),
y = c("y1", "y2"),
model = "lm",
controls = c("c1 + c2", "c3 + c4"))
# Check
distinct(specs3$specs, controls)
```

```
## # A tibble: 4 × 1
## controls
## <chr>
## 1 no covariates
## 2 c1 + c2
## 3 c3 + c4
## 4 c1 + c2 + c3 + c4
```

The `setup()`

function further has an argument
`add_to_formula`

, which allows to add covariates (or any
other formula-relevant aspects, e.g., random effect structures) to all
model functions.

```
# Add some control variables to all models
specs4 <- setup(data = example_data,
x = c("x1", "x2"),
y = c("y1", "y2"),
model = "lm",
controls = c("c1", "c2"),
add_to_formula = "c3")
# Check (see how `c3` is added to each formula, but is not part of controls)
specs4$specs[1:6,]
```

```
## # A tibble: 6 × 7
## x y model controls subsets formula model_function
## <chr> <chr> <chr> <chr> <chr> <glue> <list>
## 1 x1 y1 lm no covariates all y1 ~ x1 + 1 + c3 <fn>
## 2 x1 y1 lm c1 all y1 ~ x1 + c1 + c3 <fn>
## 3 x1 y1 lm c2 all y1 ~ x1 + c2 + c3 <fn>
## 4 x1 y1 lm c1 + c2 all y1 ~ x1 + c1 + c2 + c3 <fn>
## 5 x1 y2 lm no covariates all y2 ~ x1 + 1 + c3 <fn>
## 6 x1 y2 lm c1 all y2 ~ x1 + c1 + c3 <fn>
```

Finally, we may sometimes decide to add one of the independent or
dependent variables as covariates as well. In this case, it would not
make sense to add e.g., `x1`

as covariate if it is already
the independent variable. In this new version of specr, the
`setup()`

function automatically detects such duplications
and deletes such specifications.

```
# Adding a covariate that is also a independent or dependent variable
specs5 <- setup(data = example_data,
x = c("x1", "x2"),
y = c("y1", "y2"),
model = "lm",
controls = c("x1", "y1"))
# Check (see how only 9 specifications are kept)
specs5$specs
```

```
## # A tibble: 9 × 7
## x y model controls subsets formula model_function
## <chr> <chr> <chr> <chr> <chr> <glue> <list>
## 1 x1 y1 lm no covariates all y1 ~ x1 + 1 <fn>
## 2 x1 y2 lm no covariates all y2 ~ x1 + 1 <fn>
## 3 x1 y2 lm y1 all y2 ~ x1 + y1 <fn>
## 4 x2 y1 lm no covariates all y1 ~ x2 + 1 <fn>
## 5 x2 y1 lm x1 all y1 ~ x2 + x1 <fn>
## 6 x2 y2 lm no covariates all y2 ~ x2 + 1 <fn>
## 7 x2 y2 lm x1 all y2 ~ x2 + x1 <fn>
## 8 x2 y2 lm y1 all y2 ~ x2 + y1 <fn>
## 9 x2 y2 lm x1 + y1 all y2 ~ x2 + x1 + y1 <fn>
```

One of the most powerful arguments within the `setup()`

framework is `subsets`

, which can be used for so-called
“subset analyses”. With this argument, a variety of analytical choices
can be included.

In simple cases, we may want to investigate whether a relationship
differs across certain subgroups. In the example data, we can for
example investigate whether the relationship between `x`

and
`y`

differs across age groups (`group1`

) and
gender (`group2`

). We need to can add such subset analyses by
specifying a list in two alternative ways. The easiest way refers to
simply providing named vectors that refer to the respective variables in
the data set and their unique values:

```
list(group1 = c("young", "middle", "old),
group2 = c("female", "male"))
```

Alternatively, we can achieve the same thing by using the function
`unique()`

, which extracts the unique values from each
variable in the data set:

```
list(group1 = unique(example_data$group1),
group2 = unique(example_data$group2))
```

These lists are then passed as combinatorial factors to the expand
function within `setup()`

. If two or more grouping variables
are provided in this way (you can provide as many as you want, but it
quickly becomes messy), `setup()`

automatically adds them as
“choice” columns to the specification setup data frame. Note how it
automatically adds the value `NA`

to make sure that also the
simple subsets and not only the combinations between the two groups are
included in the specifications. It further creates a new column
“subsets”, which represents the combination of the subsetting
factors.

```
# Setup specifications
specs <- setup(data = example_data,
x = c("x1", "x2"),
y = c("y1", "y2"),
model = c("lm"),
controls = "c1",
subsets = list(group1 = unique(example_data$group1),
group2 = unique(example_data$group2)))
# Summary of specifications
summary(specs)
```

```
## Setup for the Specification Curve Analysis
## -------------------------------------------
## Class: specr.setup -- version: 1.0.1
## Number of specifications: 96
##
## Specifications:
##
## Independent variable: x1, x2
## Dependent variable: y1, y2
## Models: lm
## Covariates: no covariates, c1
## Subsets analyses: middle & female, old & female, young & female, female, middle & male, old & male, young & male, male, middle, old, young, all
##
## Function used to extract parameters:
##
## function (x)
## broom::tidy(x, conf.int = TRUE)
## <environment: 0x7f9c34e41358>
##
##
## Head of specifications table (first 6 rows):
```

```
## # A tibble: 6 × 8
## x y model controls subsets group1 group2 formula
## <chr> <chr> <chr> <chr> <chr> <fct> <fct> <glue>
## 1 x1 y1 lm no covariates middle & female middle female y1 ~ x1 + 1
## 2 x1 y1 lm no covariates old & female old female y1 ~ x1 + 1
## 3 x1 y1 lm no covariates young & female young female y1 ~ x1 + 1
## 4 x1 y1 lm no covariates female NA female y1 ~ x1 + 1
## 5 x1 y1 lm no covariates middle & male middle male y1 ~ x1 + 1
## 6 x1 y1 lm no covariates old & male old male y1 ~ x1 + 1
```

```
# Check subsets (in this case, 12 different types of subset analysis,
# including using "all" subjects)
distinct(specs$specs, subsets)
```

```
## # A tibble: 12 × 1
## subsets
## <chr>
## 1 middle & female
## 2 old & female
## 3 young & female
## 4 female
## 5 middle & male
## 6 old & male
## 7 young & male
## 8 male
## 9 middle
## 10 old
## 11 young
## 12 all
```

The true potential of this type of subsetting can only be grasped with another example. Let’s imagine we want to include the removal of outliers as an analytical choice in our specification curve analysis. Perhaps we are unsure about the cut-off value and want to investigate different (arbitrary) ones. This can again be seen as a subset analysis.

We first create variables that denote who is an outlier and who is
not according to the rule we want to use. We then pass these variables
as subsets to the `setup()`

function. This again produces
non-meaningful specifications (e.g., a subset that includes outliers, a
subset that includes people who align with different outlier rules,
etc.). So we want to keep only the meaningful specifications. In this
case, these are just 7 different types of specifications.

```
# Create variables that denote outliers (here with a range of arbitrary thresholds)
data <- data %>%
mutate(outlier1 = ifelse(y1 < mean(y1) - 2*sd(y1) | y1 > mean(y1) + 2*sd(y1), "outlier", "2.0*SD"),
outlier2 = ifelse(y1 < mean(y1) - 2.1*sd(y1) | y1 > mean(y1) + 2.1*sd(y1), "outlier", "2.1*SD"),
outlier3 = ifelse(y1 < mean(y1) - 2.2*sd(y1) | y1 > mean(y1) + 2.2*sd(y1), "outlier", "2.2*SD"),
outlier4 = ifelse(y1 < mean(y1) - 2.3*sd(y1) | y1 > mean(y1) + 2.3*sd(y1), "outlier", "2.3*SD"),
outlier5 = ifelse(y1 < mean(y1) - 2.4*sd(y1) | y1 > mean(y1) + 2.4*sd(y1), "outlier", "2.4*SD"),
outlier6 = ifelse(y1 < mean(y1) - 2.5*sd(y1) | y1 > mean(y1) + 2.5*sd(y1), "outlier", "2.5*SD"))
# Setup specs
specs <- setup(data = data,
x = c("x1", "x2"),
y = c("y1", "y2"),
model = "lm",
controls = c("c1", "c2"),
subsets = list(outlier1 = c("2.0*SD"),
outlier2 = c("2.1*SD"),
outlier3 = c("2.2*SD"),
outlier4 = c("2.3*SD"),
outlier5 = c("2.4*SD"),
outlier6 = c("2.5*SD")))
# Remove unnecessary combinations
specs$specs <- specs$specs %>%
filter(subsets == "2.0*SD" | subsets == "2.1*SD" |
subsets == "2.2*SD" | subsets == "2.3*SD" |
subsets == "2.4*SD" | subsets == "2.5*SD" |
subsets == "all")
# Check specifications (see how it contains only meaningful subsets?)
summary(specs, rows = 7)
```

```
## Setup for the Specification Curve Analysis
## -------------------------------------------
## Class: specr.setup -- version: 1.0.1
## Number of specifications: 1024
##
## Specifications:
##
## Independent variable: x1, x2
## Dependent variable: y1, y2
## Models: lm
## Covariates: no covariates, c1, c2, c1 + c2
## Subsets analyses: 2.5*SD, 2.4*SD, 2.3*SD, 2.2*SD, 2.1*SD, 2.0*SD, all
##
## Function used to extract parameters:
##
## function (x)
## broom::tidy(x, conf.int = TRUE)
## <environment: 0x7f9c34649be8>
##
##
## Head of specifications table (first 7 rows):
```

```
## # A tibble: 7 × 12
## x y model controls subsets outlier1 outlier2 outlier3 outlier4
## <chr> <chr> <chr> <chr> <chr> <fct> <fct> <fct> <fct>
## 1 x1 y1 lm no covariates 2.5*SD NA NA NA NA
## 2 x1 y1 lm no covariates 2.4*SD NA NA NA NA
## 3 x1 y1 lm no covariates 2.3*SD NA NA NA 2.3*SD
## 4 x1 y1 lm no covariates 2.2*SD NA NA 2.2*SD NA
## 5 x1 y1 lm no covariates 2.1*SD NA 2.1*SD NA NA
## 6 x1 y1 lm no covariates 2.0*SD 2.0*SD NA NA NA
## 7 x1 y1 lm no covariates all NA NA NA NA
## # ℹ 3 more variables: outlier5 <fct>, outlier6 <fct>, formula <glue>
```

```
# Run analysis and plot results
results <- specr(specs)
plot(results, choices = c("x", "y", "subsets"))
```

There are of course many more types of analytical decisions. For some more examples, see some of the other vignettes. If you have a specific type of analytical decision that you don’t know how to include, feel free to open an issue on github.