# An introduction to specr

The following vignette is a more comprehensive version of the short example on the homepage and exemplifies how to use the core functions of this package. Although using specr strictly speaking does not require any other package, we recommend to also load the tidyverse as it provides valuable functions for data wrangling and adapting outputs from specr functions. Furthermore, the tidyverse includes ggplot2 which can be used to modify the layout of the plots.

    # Load library
    library(specr)
    library(ggplot2)

## Understanding the data

In order to understand what type of analytical choices exists and how they could affect a “multiverse” of results, you need to understand your data set. In a first step, you should hence investigate your data closely. For this example, we are going to use a simulated data set (included in specr).

    # We have a look at the simulated data set that is included in the package
    head(example_data)
    #> # A tibble: 6 × 15
    #>   group1 group2 group3     x1      x2      x3     x4     c1      c2     c3
    #>   <chr>  <chr>  <chr>   <dbl>   <dbl>   <dbl>  <dbl>  <dbl>   <dbl>  <dbl>
    #> 1 middle female C       1.17  -0.363  -0.999  -0.293  0.736  0.171   0.244
    #> 2 middle male   B       0.765  0.0349  0.129  -0.155 -0.720  0.0165 -0.771
    #> 3 old    female A      -2.33  -0.998  -1.11   -1.27   0.104 -2.90   -6.95
    #> 4 old    female B      -0.507 -0.970  -0.0867 -0.978  1.79  -0.138  -0.431
    #> 5 old    male   A      -0.999  0.546   0.901   2.57  -0.245  2.02    2.83
    #> 6 middle male   A      -0.177 -1.37    0.0947 -2.53   0.315 -0.688  -1.33
    #> # … with 5 more variables: c4 <dbl>, y1 <dbl>, y2 <dbl>, y3 <dbl>, y4 <dbl>

In this example, we assume that `x` represents independent variables, `y` represents dependent variables, `c` represents control variables, and `group` denotes potential grouping variables that can be used for subsetting the data. Note that these variables are `characters`. To use them as grouping variables later, they need to be such character-variables. Numeric variables will not work and need to be transformed beforehand.

## Defining analytical choices

The next step involves setting up all specifications. This step involves an in-depth understanding of the research question and the model(s) that will be specified. In this case, we assume simply that `x` should be positively correlated with `y`. We use the function `setup()` to specify different analytical decisions.

One type of analytical choice that could additionally affect the results refers to the type of model that is estimated. The function runs traditional linear regression models by default (i.e. when `model = "lm"` is provided as argument). However, customized model functions can be passed to the function, too. The only requirement is that the customized function has `formula` and `data` as argument names. The self-made function needs to be a model estimation function, that takes the formula and estimates the model based on the data.

Once we have specified all analytic decisions, we run the function and save the results in the object `specs`. We can then use the summary function to get a quick overview of the multiverse.

    # specific model fitting function
    lm_gaussian <- function(formula, data) {
      glm(formula = formula,
          data = data,
          family = gaussian(link = "identity"))
    }

    # Specifying the analytic decisions
    specs <- setup(data = example_data,            # First, we provide the data set
                   y = c("y1", "y2"),              # We choose only one dependent variable
                   x = c("x1", "x2"),              # Two independent variables
                   model = c("lm", "lm_gaussian"), # We estimate two types of models
                   controls = c("c1", "c2"),       # We include two control variable
                   subsets = list(group1 = unique(example_data$group1),  # Subset 1
                                  group2 = unique(example_data$group2))) # Subset 2

    # Overview of the specifications/multiverse
    summary(specs, rows = 20)
    #> Setup for the Specification Curve Analysis
    #> -------------------------------------------
    #> Class:                      specr.setup -- version: 1.0.0
    #> Number of specifications:   384
    #>
    #> Specifications:
    #>
    #>   Independent variable:     x1, x2
    #>   Dependent variable:       y1, y2
    #>   Models:                   lm, lm_gaussian
    #>   Covariates:               no covariates, c1, c2, c1 + c2
    #>   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: 0x7fe4deeb4dd0>
    #>
    #>
    #> Head of specifications table (first 20 rows):
    #> # A tibble: 20 × 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
    #>  7 x1    y1    lm    no covariates young & male    young  male   y1 ~ x1 + 1
    #>  8 x1    y1    lm    no covariates male            <NA>   male   y1 ~ x1 + 1
    #>  9 x1    y1    lm    no covariates middle          middle <NA>   y1 ~ x1 + 1
    #> 10 x1    y1    lm    no covariates old             old    <NA>   y1 ~ x1 + 1
    #> 11 x1    y1    lm    no covariates young           young  <NA>   y1 ~ x1 + 1
    #> 12 x1    y1    lm    no covariates all             <NA>   <NA>   y1 ~ x1 + 1
    #> 13 x1    y1    lm    c1            middle & female middle female y1 ~ x1 + c1
    #> 14 x1    y1    lm    c1            old & female    old    female y1 ~ x1 + c1
    #> 15 x1    y1    lm    c1            young & female  young  female y1 ~ x1 + c1
    #> 16 x1    y1    lm    c1            female          <NA>   female y1 ~ x1 + c1
    #> 17 x1    y1    lm    c1            middle & male   middle male   y1 ~ x1 + c1
    #> 18 x1    y1    lm    c1            old & male      old    male   y1 ~ x1 + c1
    #> 19 x1    y1    lm    c1            young & male    young  male   y1 ~ x1 + c1
    #> 20 x1    y1    lm    c1            male            <NA>   male   y1 ~ x1 + c1

The resulting S3 class (“specr.setup”) includes a data frame with 96 different specifications. We can also see that the analysis will use the function `tidy()` from the broom package to extract parameters from the models.

We can also get a “visual summary” of the specifications and the resulting “garden of forking paths” using the generic `plot()` function.

    plot(specs, circular = TRUE)

## Fit models across specifications

The main function of the package is `specr()`. We simply pass the `specs`-object created above and specify the number of cores that should be use in evaluating all models. A good first check is to use the `summary()` function to get an overview of results.

    # Run specification curve analysis
    results <- specr(specs)

    # Summarize results
    summary(results)
    #> Results of the specification curve analysis
    #> -------------------
    #> Technical details:
    #>
    #>   Class:                          specr.object -- version: 1.0.0
    #>   Cores used:                     1
    #>   Duration of fitting process:    6.864 sec elapsed
    #>   Number of specifications:       384
    #>
    #> Descriptive summary of the specification curve:
    #>
    #>  median  mad   min  max   q25  q75
    #>    0.13 0.45 -0.49 0.68 -0.16 0.44
    #>
    #> Descriptive summary of sample sizes:
    #>
    #>  median min  max
    #>     250 160 1000
    #>
    #> Head of the specification results (first 6 rows):
    #>
    #> # A tibble: 6 × 28
    #>   x     y     model controls    subsets group1 group2 formula estimate std.error
    #>   <chr> <chr> <chr> <chr>       <chr>   <fct>  <fct>  <glue>     <dbl>     <dbl>
    #> 1 x1    y1    lm    no covaria… middle… middle female y1 ~ x…     0.6       0.1
    #> 2 x1    y1    lm    no covaria… old & … old    female y1 ~ x…     0.65      0.08
    #> 3 x1    y1    lm    no covaria… young … young  female y1 ~ x…     0.48      0.08
    #> 4 x1    y1    lm    no covaria… female  <NA>   female y1 ~ x…     0.61      0.05
    #> 5 x1    y1    lm    no covaria… middle… middle male   y1 ~ x…     0.61      0.09
    #> 6 x1    y1    lm    no covaria… old & … old    male   y1 ~ x…     0.68      0.1
    #> # … with 18 more variables: 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 <dbl>, fit_nobs <dbl>, fit_null.deviance <dbl>,
    #> #   fit_df.null <dbl>

The resulting S3 class (`specr.object”) includes relevant aspects of the specification curve analysis and a tibble that includes results for all specifications. We get a short descriptive summary of the specification curve, the sample sizes and an overview of the first 6 rows of the actual results.

## Investigating the specification curve

To investigate the results, we can use some generic functions. The simple `summary()` function has some additional functionality that we can exploit here.

    # basic descriptive summary of the entire specification curve
    summary(results,
            type = "curve")
    #> # A tibble: 1 × 7
    #>   median   mad    min   max    q25   q75   obs
    #>    <dbl> <dbl>  <dbl> <dbl>  <dbl> <dbl> <dbl>
    #> 1  0.129 0.452 -0.490 0.678 -0.161 0.440   250

    # basic descriptive summary per specific choices
    summary(results,
            type = "curve",
            group = c("x", "controls"))  # group analysis by choices
    #> # A tibble: 8 × 9
    #> # Groups:   x [2]
    #>   x     controls      median    mad      min   max     q25   q75   obs
    #>   <chr> <chr>          <dbl>  <dbl>    <dbl> <dbl>   <dbl> <dbl> <dbl>
    #> 1 x1    c1             0.117 0.709  -0.490   0.653 -0.314  0.600   250
    #> 2 x1    c1 + c2        0.160 0.595  -0.292   0.653 -0.213  0.591   250
    #> 3 x1    c2             0.178 0.609  -0.271   0.675 -0.197  0.604   250
    #> 4 x1    no covariates  0.146 0.699  -0.462   0.678 -0.314  0.616   250
    #> 5 x2    c1             0.101 0.251  -0.204   0.420 -0.0855 0.224   250
    #> 6 x2    c1 + c2        0.122 0.0970 -0.00648 0.438  0.0809 0.207   250
    #> 7 x2    c2             0.138 0.130  -0.0154  0.432  0.0663 0.240   250
    #> 8 x2    no covariates  0.102 0.251  -0.194   0.415 -0.0669 0.263   250

    # basic descriptive summary with other statistics
    summary(results,
            type = "curve",
            group = "subsets",
            stats = list(mean = mean,
                         median = median))
    #> # A tibble: 12 × 4
    #>    subsets           mean median   obs
    #>    <chr>            <dbl>  <dbl> <dbl>
    #>  1 all             0.140  0.144   1000
    #>  2 female          0.157  0.174    500
    #>  3 male            0.125  0.116    500
    #>  4 middle          0.125  0.130    331
    #>  5 middle & female 0.149  0.130    168
    #>  6 middle & male   0.0910 0.108    163
    #>  7 old             0.184  0.204    323
    #>  8 old & female    0.225  0.255    163
    #>  9 old & male      0.147  0.153    160
    #> 10 young           0.112  0.101    346
    #> 11 young & female  0.0869 0.110    169
    #> 12 young & male    0.135  0.0842   177

The output contains summary statistics such as the median, the median absolute deviation, … as well as the number of observations that were used for each model. Bear in mind that due to subsetting or missing data, sample sizes can vary considerably which, in turn, affects the results.

## Visualizing results

However, in order to grasp how the different analytical choices affect the outcome of interest (in this case, the estimate refers to the unstandardized regression coefficient b), it is reasonable to plot a specification curve. The generic function `plot()` can be used to produce the typical visualization of the specification curve and how the analytical choices affected the obtained results.

    # Plot entire visualization
    plot(results)

The resulting plot includes the ranked specification curve (A) and an overview about how the different analytical choices affect the estimate of interest (B). Red represents negative and significant effects (based on the chosen significance level, by default \(\alpha = .05\)). Blue represents positive and significant effects. Grey refers to non-significant effects.

We can also just plot the curve and adjust the style and layout using ggplot2 functions. Here, I am also order the curve by control variables and rank them in a descending order.

    # Plot
    plot(results, type = "curve", group = controls, desc = TRUE) +
      scale_color_brewer(palette = "Dark2") +
      theme_grey() +
      theme(legend.position = "none")

Sometimes, it can be useful to check the influence of specific choices on the estimate of interest more precisely. We can again use the generic function `plot()` to produce respective boxplots.

    plot(results, type = "boxplot")

We can see that the dependent variable (`y`) produces the largest differences in the obtained estimates.

## Decomposing the variance in the specification curve

Finally, we can estimate how much variance in the specification curve is related to which analytical decisions. We again can simply use the `plot()` function with the argument `type = "variance"` and receive a barplot that shows which analytical choice accounts for which amount of variance in the curve.

    plot(results, type = "variance")
    #>        grp vcov  icc percent
    #> 1  subsets 0.00 0.00    0.28
    #> 2 controls 0.00 0.01    0.87
    #> 3    model 0.00 0.00    0.00
    #> 4        y 0.16 0.83   83.01
    #> 5        x 0.00 0.01    0.73
    #> 6 Residual 0.03 0.15   15.11