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.
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.
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.
This section will familiarize you with the few differences that exist between Process and PyProcessMacro.
You can install PyProcessMacro with pip:
pip install pyprocessmacro
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()
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.
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.
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()
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.
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()
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()
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:
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.
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.
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.
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 pathsPMM_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.
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.
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.
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.
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()
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.
# 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()
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",
mods_at={"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",
mods_at={"SkillRelevance":[-1, 0, 1]},
errstyle="ci")
# 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()
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.
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:
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!
Under the hood, the plotting functions relies on a seaborn.FacetGrid
object, on which the following objects
are plotted:
plt.plot
whenerrstyle="none"
plt.plot
andplt.fill_between
whenerrstyle="band"
plt.plot
andplt.errorbar
whenerrstyle="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)
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.