Communicating Regression Results in Meaningful Terms
LSHTM R users group
3/5/2023
Amy Macdougall
The aim is to make it easier to communicate results of regressions in
meaningful terms.
Introduction
Using:
•
Predictions
•
Comparisons
•
Slopes
aka ‘marginal effects’
Introduction
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Note on terminology: 'marginal'
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Marginal mean = mean
averaged over
all covariates
vs
Conditional mean = mean
conditional on
covariates
Note on terminology: 'marginal'
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Marginal effect = the
slope
Partial derivative of the regression equation with respect to a regressor
of interest
Note on terminology: 'marginal'
Marginal effects != marginal means
•
Marginal effect = the slope
(derivative)
•
Marginal mean = average
(integral)
Both can be calculated using the
marginaleffects
package.
Note on terminology: 'marginal'
Today I’ll illustrate
some
uses of the package using a data from an
experiment carried out at the Dementia Research Centre.
1.
A model including a non-linear term.
2.
A logistic regression.
In both of these cases the
regression coefficients
may not be readily
interpretable
or the quantity of interest.
Overview
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Introducing the datset
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Binary
outcome: ‘
like
’
the colour or not
Continuous
outcome:
change in
pupil size
from baseline
Introducing the datset
1. Marginal effects for a non-linear term
Continuous outcome and predictor
Hypothesis: as time (‘trial index’) increases, pupil response may
change.
Fit a
cubic spline
to ‘trial index’ to measure non-linear effect.
How to interpret the result?
Interpreting a non-linear term - continuous outcome
Interpreting a non-linear term - continuous outcome
plot_predictions()
Interpreting a non-linear term - continuous outcome
This could be done be done with predict() + ggplot(), or
other packages.
These predictions are conditional on observed values of all
other covariates.
slopes()
Interpreting a non-linear term - continuous outcome
Interpreting a non-linear term - continuous outcome
Interpreting a non-linear term - continuous outcome
Interpreting a non-linear term - continuous outcome
Functions used so far
predictions()
plot_predictions()
Makes it easy to obtain and plot
predictions
slopes()
plot_slopes()
Uses automatic differentiation to
find the ‘marginal effect’ aka slope
and the delta method for standard
errors.
marginaleffects functions
Example 2: interpreting the results of a
logistic regression
Outcome: ‘
like
’ the colour or not
With logistic regression, the
default is to convert scale from
odds
to
probability
Logistic regression
Interpreting a non-linear term - binary outcome
(i) Continuous predictor
Difference in scale: non-linearity on one scale does not
imply non-linearity on another (interactions too).
These predictions are conditional on observed values of all
other covariates.
Interpreting a non-linear term - binary outcome
(ii) Binary predictor
avg_comparisons() makes it easy
to convert
odds ratios
to
risk
differences
1.
Find predicted probabilities for
all individuals under
both
levels
of the binary predictor.
2.
Find the
difference
between
these probabilities.
3.
Find the
mean
of these
differences.
Standard error found using the delta method, there is also a
bootstrap option.
Interpreting logistic regression - binary predictor
This is the parametric g-formula
finding the average treatment effect
(a
marginal
mean)
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Interpreting logistic regression - binary predictor
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Interpreting logistic regression - binary predictor
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Interpreting logistic regression - binary predictor
Think about assumptions!
Interpreting logistic regression - binary predictor
Functions used
predictions()
plot_predictions()
Makes it easy to obtain and plot
predictions.
slopes()
plot_slopes()
Uses automatic differentiation to find
the ‘marginal effect’ aka slope.
comparisons()
avg_comparisons()
Compares predicted values at individual
and marginal level.
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Marginal effects website
Solomon Kurt blog ‘
causal
inference with logistic regression
’
End
The aim is to facilitate the communication of regression results in an understandable manner, focusing on marginal effects and means. Explore the differences between marginal mean and conditional mean in statistics and econometrics. Learn how to calculate and interpret marginal effects in statistical analysis. Illustrate practical uses of these concepts in data analysis from an experiment conducted at the Dementia Research Centre.
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Presentation Transcript
LSHTM R users group 3/5/2023 Amy Macdougall
The aim is to make it easier to communicate results of regressions in meaningful terms. Introduction
Using: Predictions Comparisons Slopes aka marginal effects Introduction
What does marginal marginal mean? Note on terminology: 'marginal'
Marginal Marginal in statistics Marginal mean = mean averaged over all covariates vs Conditional mean = mean conditional on covariates Note on terminology: 'marginal'
Marginal Marginal in econometrics Marginal effect = the slope Partial derivative of the regression equation with respect to a regressor of interest Note on terminology: 'marginal'
Marginal effects != marginal means Marginal effect = the slope Marginal mean = average (derivative) (integral) Both can be calculated using the marginaleffects package. Note on terminology: 'marginal'
Today Ill illustrate some uses of the package using a data from an experiment carried out at the Dementia Research Centre. 1. A model including a non-linear term. 2. A logistic regression. In both of these cases the regression coefficients may not be readily interpretable or the quantity of interest. Overview
The colour spaces colour spaces experiment Introducing the datset
The colour spaces colour spaces experiment Continuous outcome: change in pupil size from baseline Binaryoutcome: like the colour or not Introducing the datset
1. Marginal effects for a non-linear term Continuous outcome and predictor Hypothesis: as time ( trial index ) increases, pupil response may change. Fit a cubic spline to trial index to measure non-linear effect. How to interpret the result? Interpreting a non-linear term - continuous outcome
plot_predictions() This could be done be done with predict() + ggplot(), or other packages. These predictions are conditional on observed values of all other covariates. Interpreting a non-linear term - continuous outcome
slopes() Interpreting a non-linear term - continuous outcome
Functions used so far predictions() slopes() plot_predictions() plot_slopes() Makes it easy to obtain and plot predictions Uses automatic differentiation to find the marginal effect aka slope and the delta method for standard errors. marginaleffects functions
Example 2: interpreting the results of a logistic regression Outcome: like the colour or not With logistic regression, the default is to convert scale from odds to probability Logistic regression
(i) Continuous predictor Difference in scale: non-linearity on one scale does not imply non-linearity on another (interactions too). These predictions are conditional on observed values of all other covariates. Interpreting a non-linear term - binary outcome
(ii) Binary predictor avg_comparisons() makes it easy to convert odds ratios to risk differences 1. Find predicted probabilities for all individuals under both levels of the binary predictor. 2. Find the difference between these probabilities. 3. Find the mean of these differences. This is the parametric g-formula finding the average treatment effect (a marginal mean) Standard error found using the delta method, there is also a bootstrap option. Interpreting logistic regression - binary predictor
Compare the effect of material medium spatial depiction spatial depiction material medium and Interpreting logistic regression - binary predictor
Compare the effect of material medium spatial depiction spatial depiction material medium and Interpreting logistic regression - binary predictor
Compare the effect of material medium spatial depiction spatial depiction material medium and Interpreting logistic regression - binary predictor
Think about assumptions! Interpreting logistic regression - binary predictor
slopes() Functions used plot_slopes() predictions() Uses automatic differentiation to find the marginal effect aka slope. plot_predictions() comparisons() Makes it easy to obtain and plot predictions. avg_comparisons() Compares predicted values at individual and marginal level.
The package is extremely extremely well documented Marginal effects website Solomon Kurt blog causal inference with logistic regression
