**From the MIT Sloan School of Management.**

**CAMBRIDGE, Mass., April 20, 2017 – **Science progresses when researchers build on prior work to extend, test, and apply theories. Aggregating the quantitative findings from prior research – meta-analysis -- plays a significant role in advancing science, however current techniques have limitations. They assume prior studies share similar substantive factors and designs, yet many studies are heterogenous. A new method, co-created by MIT Sloan School of Management Prof. Hazhir Rahmandad, solves this problem by aggregating the results of prior studies with different designs and variables into a single meta-model.

Rahmandad’s “generalized model aggregation” (GMA) may have a wide range of applications from identifying an equation for basal metabolic rate to estimating the mechanisms that moderate choice overload in marketing. His paper, *“A Flexible Method for Aggregation of Prior Statistical Findings”* which was co-authored by MIT Sloan research scientist Mohammad Jalali and Prof. Kamran Paynabar of Georgia Tech, was published last week in PLOS One.

“With a growing volume of research globally, we need methods to combine, contrast, and build on others’ work. This is reflected in the exponential growth of meta-analysis papers over the last decade,” says Rahmandad, noting that papers with the term “meta-analysis” in the title have increased 25-fold in that time. “The value of a broader method for quantitative aggregation of prior research can be immense across many disciplines.”

**Fig 1. Overview of GMA.**,

from A flexible method for aggregation of prior statistical findings, PLOS One.

For example:

- In obesity research, over 47 studies have estimated human basal metabolic rate (BMR) as a function of different body measures like fat, lean mass, age, and height. The ability to combine these into a single equation would benefit research and practice.
- In the energy sector, multiple methods exist to estimate diffuse solar energy in a location using data from distant sensors, yet there is no method for a model that aggregates these methods into a single estimating equation.
- In occupational health, studies have estimated the effectiveness of return-to-work interventions after injury or illness, but the variables in study design and methods have precluded aggregation of the findings.
- In marketing, choice overload remains a point of debate. While some studies show fewer choices lead to higher customer satisfaction, others dispute the importance of choice overload. A single model that combines prior studies could resolve this issue.

Fig 3. Aggregation of three “prior” study regressions across four scenarios,

from A flexible method for aggregation of prior statistical findings, PLOS One.

In the study, Rahmandad uses BMR as an empirical case to apply the new method. “We estimated a meta-model that incorporates the effect of all of the different body measures used in prior studies. We then compared our equation’s predictive power against older equations as well as the state-of-the-art equations from groups like the World Health Organization. We found that our equation outperforms all other equations available”

He says, “This application provides a proof of concept that the method works not only in theory but also in relevant empirical applications. The beauty is that we can find the new equation without any new data collection, as the method only uses published outcomes from prior studies.”

Rahmandad adds, “For problems that don’t yet have a clean answer, the potential for this model is major. By enabling more complex meta-analyses, GMA allows researchers to leverage previous findings to compare alternative theories and advance new models in diverse domains.”