TY - JOUR
T1 - Tutorial on removing the shackles of regression analysis
T2 - How to stay true to your theory of binary response probabilities
AU - Regenwetter, Michel
AU - Cavagnaro, Daniel R.
N1 - Funding Information:
This work was supported financially by National Science Foundation grants SES-14-59699 (Decision, Risk, and Management Science) and SES-13-0016 (Extreme Science and Engineering Discovery Environment, Pittsburgh Supercomputing Center) to Michel Regenwetter (PI). NSF had no other role other than financial and computing resources support. Both authors contributed to all aspects of this project. Both have read and approved the final article. The authors thank Ying Guo and Maria Robinson for their assistance with com- putation. Because this project only uses deidentified data from a published journal article, it is exempt from review by an Institutional Review Board (IRB). Parts of the article have been presented verbally at the July 2018 annual meeting of the Society for Mathematical Psychology. The authors are not aware of any conflicts of interest. Any statements expressed in this publication are those of the authors and need not reflect the views of their colleagues, universities, or of the National Science Foundation.
Publisher Copyright:
© 2018 American Psychological Association.
PY - 2019/4
Y1 - 2019/4
N2 - Statistical analyses of data often add some additional constraints to a theory and leave out others, so as to convert the theory into a testable hypothesis. In the case of binary data, such as yes/no responses, or such as the presence/absence of a symptom or a behavior, theories often actually predict that certain response probabilities change monotonically in a specific direction and/or that certain response probabilities are bounded from above or below in specific ways. A regression analysis is not really true to such a theory in that it may leave out parsimonious constraints and in that extraneous assumptions like linearity or log-linearity, or even the assumption of a functional relationship, are dictated by the method rather than the theory. That mismatch may well bias the results of empirical analysis and jeopardize attempts at meaningful replication of psychological research. This tutorial shows how contemporary order-constrained methods can shed more light on such questions, using far weaker auxiliary assumptions, while also formulating more detailed, nuanced, and concise hypotheses, and allowing for quantitative model selection.
AB - Statistical analyses of data often add some additional constraints to a theory and leave out others, so as to convert the theory into a testable hypothesis. In the case of binary data, such as yes/no responses, or such as the presence/absence of a symptom or a behavior, theories often actually predict that certain response probabilities change monotonically in a specific direction and/or that certain response probabilities are bounded from above or below in specific ways. A regression analysis is not really true to such a theory in that it may leave out parsimonious constraints and in that extraneous assumptions like linearity or log-linearity, or even the assumption of a functional relationship, are dictated by the method rather than the theory. That mismatch may well bias the results of empirical analysis and jeopardize attempts at meaningful replication of psychological research. This tutorial shows how contemporary order-constrained methods can shed more light on such questions, using far weaker auxiliary assumptions, while also formulating more detailed, nuanced, and concise hypotheses, and allowing for quantitative model selection.
KW - Order-constrained inference
KW - Regression
KW - Replication
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U2 - 10.1037/met0000196
DO - 10.1037/met0000196
M3 - Article
C2 - 30359043
AN - SCOPUS:85055536039
SN - 1082-989X
VL - 24
SP - 135
EP - 152
JO - Psychological Methods
JF - Psychological Methods
IS - 2
ER -