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Related Concept Videos

Regression Toward the Mean01:52

Regression Toward the Mean

Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when researchers try to extrapolate results...
Regression Analysis01:11

Regression Analysis

Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.
In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:
Multiple Regression01:25

Multiple Regression

Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
Test for Homogeneity01:23

Test for Homogeneity

The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can be stated as...
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
What are Estimates?01:06

What are Estimates?

It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
The estimate for the mean of a sample is denoted by ͞x, whereas the mean of the population is designated as μ. Further, parameters such as the mean,...

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Related Experiment Video

Updated: Jun 10, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Heterogeneous treatment effects: what does a regression estimate?

William Rhodes1

  • 1Abt Associates Inc., Cambridge, MA, USA. bill_rhodes@abtassoc.com

Evaluation Review
|July 22, 2010
PubMed
Summary

Standard regression analysis in evaluation research can obscure treatment effects with heterogeneous impacts. Alternative methods using propensity scores or hierarchical models offer clearer behavioral interpretations for researchers.

Area of Science:

  • Econometrics
  • Evaluation Research
  • Causal Inference

Background:

  • Regression analysis is commonly used in evaluation research to control for confounding factors.
  • However, standard regression models may yield treatment effect estimates lacking behavioral interpretation when treatment effects are heterogeneous, even under the selection on observables assumption.

Purpose of the Study:

  • To clarify the treatment effect identified by standard regression models under heterogeneous treatment effects.
  • To compare these with estimators from propensity score weighting and random coefficient/hierarchical models.
  • To provide guidance for evaluators on choosing appropriate methods.

Main Methods:

  • Theoretical analysis of regression models with confounding factors and heterogeneous treatment effects.

Related Experiment Videos

Last Updated: Jun 10, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

  • Examination of propensity score weighting methods.
  • Analysis of random coefficient and hierarchical models for causal inference.

    • Main Results:

    • Identifies the specific, often behaviorally uninterpretable, treatment effect estimated by standard regression.
    • Demonstrates that propensity score and hierarchical models identify behaviorally interpretable treatment effects under the same assumptions.
    • Highlights the limitations of standard regression in the presence of heterogeneous treatment effects.

    Conclusions:

    • Researchers should consider alternative models like propensity score weighting or hierarchical models for clearer interpretation of treatment effects.
    • These alternative methods are crucial when treatment effects are heterogeneous and selection on observables is assumed.
    • The study offers practical advice for improving the rigor and interpretability of evaluation research.