PyProcessMacro 1.0.12

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

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.

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.

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.

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 conditional direct and indirect effects at various levels of the moderators. See the documentation for plot_conditional_indirect_effects() and plot_conditional_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.

Version History

Master Versions

1.0.11

Various doc and bug fixes In particular, the Moderated Mediation index (MM_index_summary()) was not displayed.

1.0.8

Bug fix on plot_conditional_(in)direct effects An error warning was unnecessarily generated for some variable names. This has now been fixed.

1.0.5

Bug fix on newer numpy version A recent numpy version was causing PyProcessMacro to crash on non-float data. Thanks to William Harding for the bug report and for the fix.

1.0.4

Bug fix for standard error estimate in all models PyProcessMacro was, by default, using the HC3 estimator for the variance-covariance matrix instead of the HC0 estimator. This has now been changed. To continue using the HC3 estimator, specify hc3=True when initializing the Process instance. Thanks to Zoé Ziani for the bug report.

1.0.3

Bug fix for Models 58 and 59 The number of moderators was not properly computed, and pyprocessmacro was crashing on those two models. It has now been fixed. Thanks to amrain-py for the bug report.

1.0.2

Bug fix in the Index of Moderated Moderated Mediation In the summary, the Index of Moderated Moderated Mediation was reported as a zero-width confidence interval.

1.0.0

Added support for floodlight analysis (Johnson-Neyman region of significance).

The methods floodlight_direct_effect() and floodlight_indirect_effect() can now be used to find the range of values at which an effect is significant. See the documentation for more information on those methods.

Added methods: spotlight_direct_effect() and spotlight_direct_effect().

Those methods can be used to compute the conditional (in)direct effects of the models at various levels of the moderators.

Deprecation of plot_direct_effects() and plot_indirect_effects().

Those methods have been deprecated in favor of plot_conditional_direct_effects() and plot_conditional_indirect_effects() respectively.

The signature of the function has also changed: the argument mods_at has been renamed modval for consistency with other functions. Under the hood, those functions are faster and are using the newly introduced spotlight_direct_effect() and spotlight_direct_effect() methods.

Beta versions

0.9.6 -> 0.9.7

• Added support for Moderation Mediation Index in single moderator models.
• Performance improvements
• Dependency updates
• Added tests

0.9.1 -> 0.9.5

• Various bugfixes
• Performance improvements

0.9.0

First beta release.

Installation and Documentation

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

You can install PyProcessMacro with pip:

pip install pyprocessmacro

1. Initializing a Process object

A. Minimal example

The basic syntax for PyProcessMacro is the following:

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!

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.
• all means that the controls will be added in all equations.

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

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

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:

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.

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

2. 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.

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).

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
• MM_index_summary() returns a DataFrame of indices for Moderated Mediation, and their SE/CI, for each of the mediation paths. If the model does not compute a MM, this will return an error.
• 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.
• MMM_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.

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.

3. Spotlight and Floodlight Analysis

A. Compute direct/indirect effects for specific values (spotlight analysis)

If you wish to display the conditional effects at other values of the moderator(s), you do not have to re-instantiate the model from scratch, and can instead use the spotlight_direct_effect() and spotlight_indirect_effect() methods.

df_direct_effects = p.spotlight_direct_effect(modval={
                                    "Motivation":[-1, 0, 1], # Moderator 'Motivation' at values -1, 0 and 1
                                    "SkillRelevance":[-5, 5] # Moderator 'SkillRelevance' at values -1 and 1
            })

df_indirect_effects = p.spotlight_indirect_effect(med_name="MediationSkills", modval={
                                    "Motivation":[-1, 0, 1], # Moderator 'Motivation' at values -1, 0 and 1
                                    "SkillRelevance":[-5, 5] # Moderator 'SkillRelevance' at values -1 and 1
            })

B. Find the values of a moderator for which the direct/indirect effect are significant (floodlight analysis)

Instead of checking the direct and indirect effects at specific values, you might be interested in identifying under which level of a moderator the effect becomes significant.

floodlight_motiv_direct= p.floodlight_direct_effect(mod_name="Motivation")
floodlight_motiv_indirect = p.spotlight_indirect_effect(med_name="MediationSkills", mod_name="Motivation")

Calling floodlight_motiv_direct or floodlight_motiv_indirect will print out a detailed summary of the region(s) of significance. Alternatively, you can call floodlight_motiv_direct.get_significance_regions() to get the regions of positive/negative significance in a dictionary.

The floodlight analysis can only be conducted on one moderator at a time. When multiple moderators are present on the direct/indirect path, the floodlight analysis assumes the value of those other moderators to be zero. However, you can change this behavior by specifying a custom level for the other moderators:

floodlight_motiv_direct= p.floodlight_direct_effect(mod_name="Motivation", other_modval={"SkillRelevance": 1})
floodlight_motiv_indirect = p.spotlight_indirect_effect(med_name="MediationSkills", mod_name="Motivation",
                                                        other_modval={"SkillRelevance": 1})

Here, pyprocessmacro will conduct a floodlight analysis on the effect of MediationSkills when the level of SkillRelevance is set to 1. This is, in essence, a spotlight-floodlight analysis ;).

4. Recover 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.

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.

5. Plotting capabilities

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

The methods plot_conditional_indirect_effects() and plot_conditional_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.

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()

# 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()

# 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()

# 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 modval argument.

# Change the spotlight values for SkillRelevance
g = p.plot_indirect_effects(med_name="MediationSkills", x="Motivation", hue="SkillRelevance", 
                            modval={"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.

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

# Error band for continous moderator
g = p.plot_indirect_effects(med_name="MediationSkills", x="Motivation", hue="SkillRelevance", 
                            modval={"SkillRelevance":[-1, 0, 1]},
                            errstyle="ci")

# No representation of error
g = p.plot_indirect_effects(med_name="MediationSkills", x="Motivation", hue="SkillRelevance", 
                            modval={"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. To make sure that this is intentional, pyprocessmacro will warn you when this happens.

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 modval dictionary:

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

If you pass multiple values in modval for a moderator that is not displayed of the graph, the method will return an error.

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:

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, by the financial support of INSEAD and by the ADLPartner PhD award.