Misspecification
- Occurs when the chosen model form or assumptions do not match the true relationships in the data.
- Produces inaccurate estimates, predictions, or conclusions.
- Can be mitigated by exploratory data analysis, checking model assumptions, and selecting appropriate model specifications.
Definition
Section titled “Definition”Misspecification refers to the incorrect specification or construction of a model. In other words, it refers to the situation when the model used to analyze a particular phenomenon or data does not accurately capture the underlying relationships and patterns. This can lead to inaccurate or misleading results and conclusions.
Explanation
Section titled “Explanation”Misspecification arises when a model fails to reflect the underlying structure or characteristics of the data or when inappropriate model assumptions are used. When the model form or its assumptions are wrong, parameter estimates, predicted values, and inferential conclusions may be incorrect or misleading. Common contributing factors include failing to account for non-linear relationships and using models that assume a different data type or structure than is present.
Examples
Section titled “Examples”Linear regression applied to a non-linear relationship
Section titled “Linear regression applied to a non-linear relationship”One example of misspecification is the use of a linear regression model to analyze data that follows a non-linear relationship. For instance, consider a study that aims to examine the relationship between a person’s age and their height. If the study uses a linear regression model to analyze this data, it may not accurately capture the non-linear relationship between age and height. This can lead to incorrect estimates of the relationship and inaccurate predictions of height based on a person’s age.
In such a case, the use of a linear regression model may lead the study to conclude that there is no relationship between age and height, or that the relationship is weaker than it actually is.
Binary logistic regression applied to non-binary data
Section titled “Binary logistic regression applied to non-binary data”Another example of misspecification is the use of a binary logistic regression model to analyze data that is not binary. For instance, consider a study that aims to examine the relationship between a person’s education level and their income. If the study uses a binary logistic regression model to analyze this data, it may not accurately capture the relationship between education level and income because education level is not binary (i.e. it can have multiple categories such as high school, college, graduate, etc.). This can lead to incorrect estimates of the relationship and inaccurate predictions of income based on a person’s education level.
In this scenario, the use of a binary logistic regression model may lead the study to conclude that there is no relationship between education level and income, or that the relationship is different than it actually is.
Notes or pitfalls
Section titled “Notes or pitfalls”- Misspecification can result from failing to account for the underlying structure and characteristics of the data (for example, ignoring non-linearity).
- It can also arise from using inadequate or inappropriate model assumptions (for example, treating multi-category data as binary).
- Misspecification has significant implications for the validity and reliability of study results and conclusions.
Related terms
Section titled “Related terms”- Linear regression
- Binary logistic regression
- Model assumptions
- Exploratory data analysis