PyProcessMacro 0.9.4

A Python library for moderation, mediation and conditional process analysis. Based on Andrew F. Hayes Process Macro.

PyProcessMacro: A Python Implementation of Andrew F. Hayes' 'Process' Macro
===========================================================================

# 1. Copyright Notice for the original Process Macro

The Process Macro for SAS and SPSS, and its associated files, are copyrighted by Andrew F. Hayes. The original code
must not be edited or modified, and must not be distributed outside of
[http://www.processmacro.org](http://www.processmacro.org).

Because PyProcessMacro is a complete reimplementation of the Process Macro, and was not based on the original
code, permission was generously granted by Andrew F. Hayes to distribute PyProcessMacro under a MIT license.

This permission is not an endorsement of PyProcessMacro: all potential errors, bugs and inaccuracies are my own, and
Andrew F. Hayes was not involved in writing, reviewing, or debugging the code.

# 2. Manifest

The Process Macro by Andrew F. Hayes has helped thousands of researchers in their analysis of moderation, mediation, and
conditional processes. Unfortunately, Process was only available for proprietary softwares (SAS and SPSS), which means
that students and researchers had to purchase a license of those softwares to make use of the Macro.

Because of the growing popularity of Python in the scientific community, I decided to implement the features of the
Process Macro into an open-source library, that researchers will be able to use without relying on those proprietary
softwaress. PyProcessMacro is released under a MIT license.

# 3. Features

In the current version, PyProcessMacro replicates the following features from the original Process Macro v2.16:
* All models (1 to 76), with the exception of Model 6 (serial mediation) are supported, and have been numerically
tested for accuracy against the output of the original Process macro (see the `test_models_accuracy.py`)
* Estimation of binary/continuous outcome variables. The binary outcomes are estimated in Logit using the
Newton-Raphson convergence algorithm, the continuous variables are estimated using OLS.
* All statistics reported by Process:
* Variable parameters for outcome models
* (Conditional) direct and indirect effects
* Indices for Partial/Conditional/Moderated Moderated Mediation are always reported if the model supports them.
* Automatic generation of spotlight values for continuous/discrete moderators.
* Rich set of options to tweak the estimation and display of the different models: (almost) all the options from
Process exist in PyProcessMacro. Check the doc for more details.

The following changes and improvements have been made from the original Process Macro:
* Variable names can be of any length, and even include spaces and special characters.
* All mediation models support an infinite number of mediators (versus a maximum of 10 in Process).
* Normal theory tests for the indirect effect(s) are not reported, as the bootstrapping approach is now widely
accepted and in most cases more robust.
* Plotting capabilities: PyProcessMacro can generate the plot of direct and indirect effects at various levels
of the moderators. See the documentation for plot_indirect_effects() and plot_direct_effects().
* Fast estimation process: PyProcessMacro leverages the capabilities of NumPy to efficiently compute a large number
of bootstrap estimates, and dramatically speed up the estimation of complex models.
* Transparent bootstrapping: PyProcessMacro explicitely reports the number of bootstrap samples that have been
discarded because of numerical instability.

In the current version, the following features have not yet been ported to PyProcessMacro:
* Support for categorical independent variables.
* Generation of individual fixed effects for repeated measures.
* R² improvement from moderators in moderation models (1, 2, 3).
* Estimation of serial mediation (Model 6)
* Some options (`normal`, `varorder`, ...). PyProcessMacro will issue a warning to tell you if an option you are
trying to use is not implemented.


# 4. Installation and Usage

This section will familiarize you with the few differences that exist between Process and PyProcessMacro.

You can install PyProcessMacro with pip:

pip install pyprocessmacro

## A. Minimal example

The basic syntax for PyProcessMacro is the following:

````python
from pyprocessmacro import Process
import pandas as pd
df = pd.read_csv("MyDataset.csv")
p = Process(data=df, model=13, x="Effort", y="Success", w="Motivation", z="SkillRelevance",
m=["MediationSkills", "ModerationSkills"])
p.summary()
````

[Click to see a sample output!](SampleOutput.md)

As you can see, the syntax for PyProcessMacro is (almost) identical to that of Process. Unless this documentation
mentions otherwise, you can assume that all the options/keywords from Process exist in PyProcessMacro.

A `Process` object is initialized by specifying a data source, the model number, and the mapping between the symbols
and the variable names.

Once the object is initialized, you can call its `summary()` method to display the estimation results

You might have noticed that there is no argument `varlist` in PyProcessMacro. This is because the list of variables
is automatically inferred from the variable names given to x, y, m.

## B. Adding statistical controls

In Process, the controls are defined as "any argument in the varlist that is not the IV, the DV, a moderator, or
a mediator." In PyProcessMacro, the list of variables to include as controls have to be explicitely specified in
the "controls" argument.

The equation(s) to which the controls are added is specified through the `controls_in` argument:
* `x_to_m` means that the controls will be added in the path from the IV to the mediator(s) only.
* `all_to_y` means that the controls will be added in the path from the IV and the mediators to the DV only.
* `both` means that the controls will be added in both equations.

The ability to specify a different list of control for each equation is coming in the next release of PyProcessMacro.

````python
p = Process(data=df, model=13, x="Effort", y="Success", w="Motivation", z="SkillRelevance",
m=["MediationSkills", "ModerationSkills"],
controls=["Control1", "Control2"],
controls_in="both")
p.summary()
````

## C. Logistic regression for binary outcomes

The original Process Macro automatically uses a Logistic (instead of OLS) regression when it detects a binary outcome.

PyProcessMacro prefers a more explicit approach, and requires you to set the parameter `logit` to `True` if your DV
should be estimated using a Logistic regression.

````python
p = Process(data=df, model=13, x="Effort", y="Success", w="Motivation", z="SkillRelevance",
m=["MediationSkills", "ModerationSkills"], logit=True)
p.summary()
````

It goes without saying that this will return an error if your DV is not dichotomous.

## D. Specifying custom spotlight values for the moderator(s)

In Process as in PyProcessMacro the spotlight values of the moderators are defined as follow:
* By default, the spotlight values are equal to M - 1SD, M and M + 1SD, where M and SD are the mean and standard
deviation of that variable. If the option `quantile=1` is specified, then the spotlight values for each moderator
are the 10th, 25th, 50th, 75th and 90th percentile of that variable.
* If a moderator is a discrete variable, the spotlight values are those discrete values.

In Process, custom spotlight values can be applied to each moderator q, v, z, ... through the arguments qmodval,
vmodval, zmodval...

In PyProcessMacro, the user must instead supply custom values for each moderator in a dictionary
passed to the `modval` parameter:

````python
p = Process(data=df, model=13, x="Effort", y="Success", w="Motivation", z="SkillRelevance",
m=["MediationSkills", "ModerationSkills"],
modval={
"Motivation":[-5, 0, 5], # Moderator 'Motivation' at values -5, 0 and 5
"SkillRelevance":[-1, 1] # Moderator 'SkillRelevance' at values -1 and 1
})
p.summary()
````


## E. Suppress the initialization information

When the Process object is initialized by Python, it displays various information about the model (model number, list of
variables, sample size, number of bootstrap samples, etc...). If you wish not to display this information, just add the
argument `suppr_init=True` when initializing the model.

````python
p = Process(data=df, model=13, x="Effort", y="Success", w="Motivation", z="SkillRelevance",
m=["MediationSkills", "ModerationSkills"], suppr_init=True)
p.summary()
````

# 4. Accessing the estimation results

After the `Process` object is initialized, you are not limited to printing the summary. PyProcessMacro implements the
following methods that allow you to conveniently recover the different estimates of interest:

## A. `summary()`

This method replicates the output that you would see in Process, and displays the following information:
* Model summaries and parameters estimates for all outcomes (i.e. the independent variable, and the mediator(s)).
* If the model has a moderation, conditional effects at the spotlight values of the moderator(s).
* If the model has a mediation, direct and indirect effects.
* If the model has a moderation and a mediation, conditional direct and indirect effects at values of the moderator(s).
* If those statistics are relevant, indices for partial, conditional, and moderated moderated mediation will be
reported.

## B. `outcome_models`

This command gives you individual access to each of the outcome models through a dictionary. This allows you to recover
the model and parameters estimates for each outcome.

Each OutcomeModel object has the following methods:
* `summary()` prints the full summary of the model (as Process does).
* `model_summary()` returns a DataFrame of goodness-of-fit statistics for the model.
* `coeff_summary()` returns a DataFrame of estimate, standard error, corresponding z/t, p-value, and
confidence interval for each of the parameters in the model.
* `estimation_results` gives you access to a dictionary containing all the statistical information of the
model.

````python
p = Process(data=df, model=13, x="Effort", y="Success", w="Motivation", z="SkillRelevance",
m=["MediationSkills", "ModerationSkills"], suppr_init=True)

model_medskills = p.outcome_models["MediationSkills"] # The model for the outcome "MediationSkills"

model_medskills.summary() # Print the summary for this model

df_params_med1 = model_medskills.coeff_summary() # Store the DataFrame of estimates into a variable.

med1_R2 = model_medskills.estimation_results["R2"] # Store the R² of the model into a variable.
````

Note that the methods are called from the `model_medskills` object! If you call `p.coeff_summary()`,
you will get an error.

## C. `direct_model`

When the Process model includes a mediation, the direct effect model can conveniently be accessed, which
gives you access to the following methods:

* `summary()` prints the full summary of the direct effects, as done in calling Process.summary().
* `coeff_summary()` returns a DataFrame of estimate, standard error, t-value, p-value, and confidence
interval for each of the (conditional) direct effect(s).

````python
p = Process(data=df, model=13, x="Effort", y="Success", w="Motivation", z="SkillRelevance",
m=["MediationSkills", "ModerationSkills"], suppr_init=True)

direct_model = p.direct_model # The model for the direct effect

df_params_direct = direct_model.coeff_summary() # Store the DataFrame of estimates into a variable.
````

Note that the methods are called from the `direct_model` object! If you call `p.coeff_summary()`, you will get an
error.


## D. `indirect_model`

When the Process model includes a parallel mediation, the indirect effect model can be accessed as well, which
gives you access to the following methods:

* `summary()` prints the full summary of the indirect effects, and other related indices, as done in
calling Process.summary().
* `coeff_summary()` returns a DataFrame of indirect effect(s) and their SE/CI for each of the mediation
paths
* `PMM_index_summary()` returns a DataFrame of indices for Partial Moderated Mediation, and their
SE/CI, for each of the moderators and mediation paths. If the model does not compute a PMM, this will return an error.
* `CMM_index_summary()` returns a DataFrame of indices for Conditional Moderated Mediation, and their
SE/CI, for each of the moderators and mediation paths. If the model does not compute a CMM, this will return an error.
* `CMM_index_summary()` returns a DataFrame of indices for Moderated Moderated Mediation, and their
SE/CI, for each of the mediation paths. If the model does not compute a MMM, this will return an error.

````python
p = Process(data=df, model=13, x="Effort", y="Success", w="Motivation", z="SkillRelevance",
m=["MediationSkills", "ModerationSkills"], suppr_init=True)

indirect_model = p.indirect_model # The model for the direct effect

df_params_direct = indirect_model.coeff_summary() # Store the DataFrame of estimates into a variable.
````

Note that the methods are called from the `indirect_model` object! If you call `p.coeff_summary()`, you will get an
error.

# 5. Bootstrap samples estimates

The original Process macro allows you to save the parameter estimates for each bootstrap sample by specifying the `save`
keyword. The Macro then returns a new dataset of bootstrap estimates.

In PyProcessMacro, this is done by calling the method `get_bootstrap_estimates()`, which returns a DataFrame containing
the parameters estimates for all variables in the model, for each outcome.

````python
p = Process(data=df, model=13, x="Effort", y="Success", w="Motivation", z="SkillRelevance",
m=["MediationSkills", "ModerationSkills"], suppr_init=True)

boot_estimates = p.get_bootstrap_estimates() # Called from the Process object directly.
````

# 6. Plotting capabilities

PyProcessMacro allows you to plot the conditional direct and indirect effect(s), at different values of the moderators.

The methods `plot_indirect_effects()` and `plot_direct_effects()` are identical in syntax, with one
small exception: you must specify the name of the mediator for `plot_indirect_effects` as a first argument. They return
a `seaborn.FacetGrid` object that can be used to further tweak the appearance of the plot.

## A. Basic Usage

When plotting conditional direct (and indirect) effects, the effect is always represented on the y-axis.

The various spotlight values of the moderator(s) can be represented on several dimensions:
* On the x-axis (moderator passed to `x`).
* As a color-code, in which case several lines are displayed on the same plot (moderator passed to `hue`).
* On different plots, displayed side-by-side (moderator passed to `col`).
* On different plots, displayed one below the other (moderator passed to `row`)

At the minimum, the `x` argument is required, while the `hue`, `col` and `row` are optional.
The examples below are showing what the plots could look like for a model with two moderators.

````python
from pyprocessmacro import Process
import pandas as pd
import matplotlib.pyplot as plt

df = pd.read_csv("MyDataset.csv")
p = Process(data=df, model=13, x="Effort", y="Success", w="Motivation", z="SkillRelevance",
m=["MediationSkills", "ModerationSkills"], suppr_init=True)

# Conditional direct effects of Effort, at values of Motivation (x-axis)
g = p.plot_direct_effects(x="Motivation")
plt.show()
````

````python
# Conditional indirect effects through MediationSkills, at values of Motivation (x-axis) and
# SkillRelevance (color-coded)
g = p.plot_indirect_effects(med_name="MediationSkills", x="Motivation", hue="SkillRelevance")
g.add_legend(title="") # Add the legend for the color-coding
plt.show()
````
````python
# Display the values for SkillRelevance on side-by-side plots instead.
g = p.plot_indirect_effects(med_name="MediationSkills", x="Motivation", col="SkillRelevance")
plt.show()
````
````python
# Display the values for SkillRelevance on vertical plots instead.
g = p.plot_indirect_effects(med_name="MediationSkills", x="Motivation", row="SkillRelevance")
plt.show()
````
## B. Change the spotlight values

By default, the spotlight values used to plot the effects are the same as the ones passed when initializing Process.
However, you can pass custom values for some, or all, the moderators through the `mods_at` argument.

````python
# Change the spotlight values for SkillRelevance
g = p.plot_indirect_effects(med_name="MediationSkills", x="Motivation", hue="SkillRelevance",
mods_at={"SkillRelevance": [-5, 5]})
g.add_legend(title="")
plt.show()
````

## C. Representation of uncertainty

The display of confidence intervals for the direct/indirect effects can be customized through the `errstyle` argument:
* `errstyle="band"` (default) plots a continuous error band between the lower and higher confidence interval. This
representation works well when the moderator displayed on the x-axis is continuous (e.g. age), as it allows you to
visualize the error at all levels of the moderator.
* `errstyle="ci"` plots an error bar at each value of the moderator on x-axis. It works well when the moderator
displayed on the x-axis is dichotomous or has few values (e.g. gender), as it reduces clutter.
* `errstyle="none"` does not show the error on the plot.

````python
# CI for dichotomous moderator
g = p.plot_indirect_effects(med_name="MediationSkills", x="Motivation", hue="SkillRelevance",
mods_at={"Motivation": [0, 1], "SkillRelevance":[-1, 0, 1]},
errstyle="ci")
````

````python
# Error band for continous moderator
g = p.plot_indirect_effects(med_name="MediationSkills", x="Motivation", hue="SkillRelevance",
mods_at={"SkillRelevance":[-1, 0, 1]},
errstyle="ci")
````
````python
# No representation of error
g = p.plot_indirect_effects(med_name="MediationSkills", x="Motivation", hue="SkillRelevance",
mods_at={"SkillRelevance":[-1, 0, 1]},
errstyle="none")

plt.show()
````


## D. "Partial" plots

So far, the number of moderators supplied as arguments to the plot function was always equal to the number of moderators
on the path of interest (1 for the direct path, 2 for the indirect path).

You can also "omit" some moderators, and plot "partial" conditional direct/indirect effects. In that case, the omitted
moderators will assume a value of 0 when computing the direct/indirect effects.

````python
p = Process(data=df, model=13, x="Effort", y="Success", w="Motivation", z="SkillRelevance",
m=["MediationSkills", "ModerationSkills"], suppr_init=True)

# SkillRelevance is a moderator of the indirect path, but is not mentioned as an argument in the plotting function!
g = p.plot_indirect_effects(med_name="MediationSkills", x="Motivation")
plt.show() # This plot represents the "partial" conditional indirect effect, when SkillRelevance is evaluated at 0.
````


If you want the omitted moderator(s) to have a different value than 0, you must pass a unique value for each moderator
as a key in the `mods_at` dictionary:

````python
g = p.plot_indirect_effects(med_name="MediationSkills", x="Motivation", mods_at={"SkillRelevance":[-5]})
plt.show() # This plot represents the "partial" conditional indirect effect, when SkillRelevance is evaluated at -5.
````

Do not pass multiple values in `mods_at` if you do not intend to represent this moderator on the plot, as the graph
will then not be interpretable!

# E. Customize the appearance of the plots

Under the hood, the plotting functions relies on a `seaborn.FacetGrid` object, on which the following objects
are plotted:
* `plt.plot` when `errstyle="none"`
* `plt.plot` and `plt.fill_between` when `errstyle="band"`
* `plt.plot` and `plt.errorbar` when `errstyle="ci"`

You can pass custom arguments to each of those objects to customize the appearance of the plot:

````python
from pyprocessmacro import Process
import pandas as pd
import matplotlib.pyplot as plt

df = pd.read_csv("MyDataset.csv")
p = Process(data=df, model=13, x="Effort", y="Success", w="Motivation", z="SkillRelevance",
m=["MediationSkills", "ModerationSkills"], suppr_init=True)

plot_kws = {'lw': 5} # Plot: Make the lines bolder
err_kws = {'capthick': 5, 'ecolor': 'black', 'elinewidth': 5, 'capsize': 5} # Errors: Make the CI bolder and black
facet_kws = {'aspect': 1} #Grid: Make the FacetGrid a square rather than a rectangle


g = p.plot_indirect_effects(med_name="MediationSkills", x="Motivation", errstyle="ci",
plot_kws=plot_kws, err_kws=err_kws, facet_kws=facet_kws)
````

# 7. About
PyProcessMacro was developed by Quentin André during his PhD in Marketing at INSEAD Business School, France.

His work on this library was made possible by Andrew F. Hayes'
[excellent book](http://afhayes.com/introduction-to-mediation-moderation-and-conditional-process-analysis.html),
by the financial support of INSEAD and by the ADLPartner PhD award.