STATISTICAL METHODS
Regression & Predictive Modeling
Statistical Consulting for Outcome Modeling
Our regression analysis consulting starts from the outcome you measured, whether continuous, binary, count, ordinal or categorical, and from how the data were collected, then applies the model family that fits, from linear and logistic regression to mediation and moderation.
Regression & Predictive Modeling is the family of regression modeling methods that relate an outcome to one or more predictors, to estimate adjusted associations, examine proposed mechanisms or predict outcomes for new cases. Within Statistical Methods, these methods are separated by the outcome type, which sets the family of generalized linear models, by the number and structure of the predictors and by whether the aim is explanation or prediction. OnlineSPSS is a specialist statistical consultancy for academic, clinical and professional research, and the analysis is carried out in-house by PhD-level statisticians.
METHODS IN THIS CATEGORY
Regression & Predictive Modeling Methods
Thirteen methods for regression modeling: linear models for continuous outcomes, generalized linear models for binary, categorical, ordinal and count outcomes, and models for indirect and conditional effects.
01
Simple Linear Regression
Models a continuous outcome as a line in one predictor, reporting the slope and intercept with confidence intervals and residual diagnostics.
Single predictor
Slope
02
Multiple Linear Regression
Models a continuous outcome from several predictors, giving adjusted coefficients with checks on residuals, influence and collinearity.
Adjusted effects
Diagnostics
03
Hierarchical Regression
Enters predictors in theory-based blocks and tests the change in R squared, with the order of the blocks justified before the results.
Blocks
R squared change
04
Non-Parametric Regression
Fits splines, LOESS or additive models to a curved relationship, with the smoothing chosen by validation and uncertainty bands shown.
Flexible curves
Smoothing
05
Logistic Regression
Models a binary outcome from several predictors, reporting odds ratios with intervals and judging fit by calibration and discrimination.
Binary outcome
Odds ratios
06
Multinomial Logistic Regression
Models an outcome with three or more unordered categories against a reference category, with the sample size checked for each category.
Nominal outcome
Reference
07
Ordinal Regression
Models an ordered outcome such as a rating scale with cumulative odds, and checks the proportional odds assumption before reporting.
Ordered outcome
Cumulative odds
08
Firth's Logistic Regression
Gives finite, less biased estimates for a binary outcome with rare events or separation, using a penalized likelihood.
Rare events
Separation
09
Poisson Regression
Models counts or rates with an exposure offset, giving incidence rate ratios and checking the assumption that the variance equals the mean.
Count outcome
Rate ratios
10
Negative Binomial Regression
Models overdispersed counts whose variance exceeds the mean, with a dispersion parameter and rate ratios reported with intervals.
Overdispersion
Counts
11
Mediation Analysis
Estimates the indirect effect of a predictor through an intermediate variable, with a bootstrap interval and the causal assumptions stated.
Indirect effect
Pathway
12
Moderation Analysis
Tests whether the effect of one predictor depends on another through an interaction term, probed at meaningful values of the moderator.
Interaction
Conditional effect
13
Moderated Mediation
Examines whether an indirect effect varies across levels of a moderator, using conditional indirect effects and an index of moderated mediation.
Conditional
Indirect effect
METHOD COMPARISON
Choosing Between Methods in This Family
Start from the outcome type, then the predictors and the aim; regression model selection should follow the research question and validation, not whichever variables reach significance.
| Research situation | Typical method |
|---|---|
| Continuous outcome, one predictor | Simple Linear Regression |
| Continuous outcome, several predictors, adjusted effects | Multiple Linear Regression |
| Predictors entered in theory-based blocks | Hierarchical Regression |
| Curved relationship of unknown shape | Non-Parametric Regression |
| Binary outcome | Logistic Regression |
| Binary outcome with rare events or separation | Firth’s Logistic Regression |
| Outcome with three or more unordered categories | Multinomial Logistic Regression |
| Ordered outcome, such as a rating scale | Ordinal Regression |
| Counts or rates with variance close to the mean | Poisson Regression |
| Overdispersed counts | Negative Binomial Regression |
| Effect of a predictor transmitted through an intermediate variable | Mediation Analysis |
| Effect of a predictor that depends on another variable | Moderation Analysis |
| Indirect effect that depends on a moderator | Moderated Mediation |
COMMON ANALYTICAL ISSUES
Common Issues We See in Regression & Predictive Modeling
Most regression errors arise before a coefficient is read, in how the outcome, the functional form and the purpose of the model were defined.
Outcome Type Forced Into a Linear Model Binary, count and ordinal outcomes analyzed with ordinary linear regression give impossible predictions, wrong variance assumptions and misleading intervals. The outcome type, not habit, selects the model family.
Coefficients Read Before Diagnostics Functional form, influential cases, collinearity, sparse categories and separation can each change what a coefficient means, so they are checked before any estimate is interpreted or any p-value quoted.
Prediction Judged as Explanation A prediction model is judged by discrimination, calibration and validation on new data, not by significant coefficients, while an explanatory model needs a defensible adjustment set and cautious causal wording.
Model Selection by Significance Stepwise selection and a search for significant predictors overfit the sample and bias estimates away from zero. Selection should follow the research question, prespecified covariates and validation.
Unsure which model fits your outcome and design? We can review the question, the data and the predictors and confirm an appropriate approach.
ANALYTICAL SUPPORT
From Method Selection to Reportable Results
As part of our Quantitative Data Analysis service, regression analysis consulting takes a model from the choice of family to coefficients reported with confidence intervals.
Method Specification We confirm the outcome type, the unit of analysis, the predictors and the purpose, explanation or prediction, and document why the chosen model family fits.
Assumptions & Diagnostics Functional form, influential cases, collinearity, sparse categories, dispersion and separation are examined through plots and diagnostics, not through one significance test.
Effect Estimates & Uncertainty Results are reported as coefficients, odds ratios, rate ratios or indirect effects with confidence intervals, and prediction models with discrimination, calibration and validation.
Publication-Ready Outputs Tables and figures follow APA 7, STROBE, TRIPOD for prediction models or the journal's requirements, with syntax or scripts provided where applicable.
SOFTWARE
Statistical Software for Regression Modeling
Each model is run in the software that fits the outcome type and the project's reproducibility needs, with syntax or scripts provided where applicable.
RESEARCH DISCIPLINES
Regression Modeling Across Research Fields
Regression is used wherever an outcome is related to explanatory factors, and each field brings its own outcome types, covariates and reporting conventions.
RESEARCHER VOICE
What Researchers Say
Feedback from two researchers, on focusing a regression on specification and interpretation, and on starting from the experimental unit and the data-generating process.
“We had several predictors and a clear outcome, but the model choice was less obvious once non-linearity, interactions, sparse categories, and diagnostics were considered. The team focused on specification and interpretation rather than just significance, which made the final regression much easier to defend.”
“We needed someone comfortable with biological data where technical replicates, skewed measures, detection limits, and small experimental groups can change the analysis completely. The team focused on the experimental unit and data-generating process first, which gave us much more confidence in the final results.”
OnlineSPSS provides the agreed methodological, analytical and statistical reporting support and claims no intellectual contribution. The research question, interpretation, conclusions and authorship remain with the researcher or research team.
FREQUENTLY ASKED QUESTIONS
Questions About Regression & Predictive Modeling
Short answers to what researchers ask before sharing a regression project, from choosing a model to confidentiality and the assessment process.
Which regression model should I use for my outcome?
The outcome type sets the model family: linear regression for a continuous outcome, logistic for a binary one, multinomial or ordinal for categories, and Poisson or negative binomial for counts. The predictors, clustering and purpose then refine the choice. If a regression has already been run and questioned, Independent Statistical Review looks again at the model and how it was reported.
Is a prediction model judged like an explanatory model?
No. An explanatory model is judged by whether its adjusted estimates are interpretable and defensible, while a prediction model is judged by discrimination, calibration and validation on data not used to fit it. A model with significant coefficients can still predict poorly, and a good predictor need not have coefficients that carry a causal meaning.
How do you protect my research data and confidentiality?
Datasets, model code, output files and project details are handled confidentially, and project information is not published. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
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