Concept Architecture
Concept
Theoretically, Model Fit describes the degree to which a statistical model reproduces the observed data. It reflects the extent to which the model captures the underlying relationships between explanatory variables and outcomes while balancing explanatory performance and model complexity. Model fit is fundamental to statistical inference and prediction because an inadequately fitting model may produce biased parameter estimates and unreliable predictions. In health economics, model fit is assessed when developing regression models, survival models, risk equations and utility mapping models that inform economic evaluations.
Mathematically, model fit is quantified using statistical measures that compare observed outcomes with those predicted by the fitted model. The appropriate measure depends on the modelling framework and may include the coefficient of determination, likelihood functions, deviance, residual error or information criteria. These statistics summarise how closely the fitted model approximates the observed data while recognising that increasing model complexity does not necessarily improve predictive performance.
In practice, model fit is evaluated by examining numerical fit statistics together with graphical diagnostics and residual analyses. Health economists assess model fit before selecting statistical models used to estimate costs, health outcomes, treatment effects or transition probabilities for decision-analytic models. Assessment typically considers both predictive accuracy and the plausibility of the resulting parameter estimates.
Purpose
Used to quantify how well a statistical model represents observed data, compare alternative model specifications and support the selection of reliable models for health economic evaluation.
Mathematical Formulae
Primary Formula
For linear regression, the canonical measure of model fit is the coefficient of determination:
R� = 1 ? [�???� (y? ? ??)�] / [�???� (y? ? ?)�]
where:
- y? = observed value
- ?? = predicted value
- ? = mean observed value
Supporting Formulae
Residual Sum of Squares:
RSS = �???� (y? ? ??)�
Log-likelihood:
?(?) = �???� ln f(y? | ?)
Related Mathematical Methods
- Coefficient of determination (R�)
- Adjusted R�
- Residual analysis
- Maximum likelihood estimation
- Akaike Information Criterion
- Bayesian Information Criterion
- Likelihood ratio test
- Goodness of fit testing
Example
A health economist develops a regression model predicting annual healthcare costs using age, disease severity and comorbidity.
The total variation in costs is:
TSS = 4,800,000
The residual variation is:
RSS = 960,000
Therefore,
R� = 1 ? 960,000 / 4,800,000 = 0.80
The fitted model explains 80% of the observed variation in healthcare costs, indicating good model fit.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| RSQ | =RSQ(B2:B501,C2:C501) | Calculates the coefficient of determination between observed and predicted outcomes. |
| SUMXMY2 | =SUMXMY2(B2:B501,C2:C501) | Calculates residual variation between observed and predicted values. |
| DEVSQ | =DEVSQ(B2:B501) | Calculates the total variation in observed outcomes. |
| AVERAGE | =AVERAGE(B2:B501) | Calculates the mean observed outcome required for total variation calculations. |
VBA (Optional)
Automate calculation of multiple model fit statistics and generate comparative reports for competing statistical models.
Sources
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- Harrell FE. Regression Modeling Strategies. 2nd ed.
- Burnham KP, Anderson DR. Model Selection and Multimodel Inference. 2nd ed.
- Hastie T, Tibshirani R, Friedman J. The Elements of Statistical Learning.
- ISPOR Good Practice Reports on statistical modelling and validation.
Related Concepts (2)
Library
Publications
1
Model Transparency and Validation: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-7 — Eddy, Hollingworth, Caro, Tsevat, McDonald & Wong, Task Force Report 7 ed., 2012 (Value in Health / Medical Decision Making)
Best-practice guidance on model transparency and validation, defining face, internal, external and predictive validation and setting out how models should be documented for scrutiny.
Journal ArticleView source →
Frequently Asked Questions (6)
What is model fit?
The degree to which a statistical or structural model's predictions correspond to observed data, used to judge whether a specification is adequate.
Source: Eddy DM, Hollingworth W, Caro JJ, et al. Model transparency and validation: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-7. Value in Health. 2012;15(6):843-850. doi:10.1016/j.jval.2012.04.012.
How does model fit relate to a model's purpose?
How closely a model needs to match observed data depends on what it is for. A model meant to reproduce a survival curve precisely must fit that curve well, whereas one meant only to rank options by broad value can tolerate looser agreement. Fit is therefore judged against the demands of the decision rather than as an absolute virtue, and a fit good enough for one purpose may be inadequate for another. The required standard follows from the question the model must answer. Hastie and colleagues (2009) discuss fit in context.
Source: Hastie et al. 2009
How is model fit assessed?
Model fit is assessed by comparing the model's predictions with observed data, using goodness-of-fit statistics that quantify the discrepancy and visual comparison of predicted against observed values. Smaller discrepancies indicate better fit. For statistical models, measures such as the chi-squared statistic or fit indices are used, and for models fitted to targets, the agreement with those targets is examined. The assessment shows how closely the model matches the data, informing whether the specification is adequate.
Source: Pearson 1900
Why does model fit matter?
Model fit matters because a model is useful only if it adequately represents the data or system it is meant to capture, so how well its predictions match observations indicates whether the specification is sound. Poor fit signals that the model is misspecified or missing important features, so its results may be unreliable. Assessing fit informs whether a model is adequate and helps choose among alternatives, though good fit must be weighed against complexity and generalisation, since fitting the data closely is not sufficient alone.
Source: Akaike 1974
How does model fit relate to model complexity?
Model fit relates to complexity because a more complex model, with more parameters, can always fit observed data at least as well, so fit alone would favour complexity, risking overfitting where the model captures noise and predicts poorly on new data. Judging a model requires balancing fit against parsimony, using criteria that penalise complexity, such as the Akaike information criterion. Good model fit is therefore assessed alongside the number of parameters, seeking a specification that fits well without unnecessary complexity.
Source: Akaike 1974
What does poor model fit indicate?
Poor model fit indicates that the model's predictions do not correspond well to the observed data, suggesting the specification is inadequate, missing important features, or misrepresenting the relationships, so its results may be unreliable. It signals that the model should be reconsidered, perhaps by revising its structure or adding relevant terms. Poor fit is a warning that the model does not capture the pattern in the data, prompting investigation and improvement before the model's predictions are relied upon.
Source: Eddy et al. 2012
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 15 Oct 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/model-fit
- Term code
- HE-EM-MV-045
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