# Parameter estimates

Parameter estimates (also called coefficients) are the log odds ratio associated with a one-unit change of the predictor, all other predictors being held constant.

The unknown model parameters are estimated using maximum-likelihood estimation.

A coefficient describes the size of the contribution of that predictor; a large coefficient indicates that the variable strongly influences the probability of that outcome, while a near-zero coefficient indicates that variable has little influence on the probability of that outcome. A positive sign indicates that the explanatory variable increases the probability of the outcome, while a negative sign indicates that the variable decreases the probability of that outcome. A confidence interval for each parameter shows the uncertainty in the estimate.

When the model contains categorical variables, the interpretation of the coefficients is more complex. For each term involving a categorical variable, a number of dummy predictor variables are created to predict the effect of each different level. There are different ways to code the predictors for a categorical variable, the most common method in logistic regression is called *reference cell coding* or *dummy coding*. In reference cell coding, the first category acts as a
baseline, and you can interpret the other coefficients as an increase or decrease in the log odds ratio over the baseline category.

**Available in Analyse-it Editions**

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- What is Analyse-it?
- What's new?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Compare groups
- Compare pairs
- Contingency tables
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Linear fit
- Logistic fit
- Generalized linear models
- Fitting a simple logistic regression
- Fitting an advanced logistic model
- Fitting a simple probit regression
- Parameter estimates
- Odds ratio estimates
- Effect of model hypothesis test
- Effect of term hypothesis test
- Study design
- Method comparison
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 5.65

Published 14-Aug-2020