A** free parameter **is one which is not pre-defined by the model, but which can be chosen or estimated based on theoretical ideas or experimental data. Other types of parameters include fixed and constrained.

**Fixed parameters**are completely defined by the model; for example, if your model defines a parameter j = 5, j is fixed.**Constrained parameters**are restricted to an interval but not completely defined. For instance, if your model defines the parameter k as between 0 and 1, it is a constrained parameter.

## Examples of Free Parameters

If your model suggests that A is proportional to B (i.e. A = Bk), the proportionality constant k is a a free parameter. If, instead, our model stated that A = 2*B, we would only have fixed parameters to work with.

If our model states that y and x are related by the equation y = ax^{2}+ bx + c, then *a*, *b*, and *c* are all free parameters.

## Why To Use Free Parameters—and Why To Avoid Them

We can always add free parameters to a model; and the more we add, the closer our model may seem to fit the data. But with enough arbitrary parameters, a model may be made to fit any data set; there is a big danger of free parameters moving us away from reality and into the realm of wishful thinking. In scientific modeling we **try to keep the number of free parameters to a minimum**.

If the number of free parameters in a model is the same as the number of distinct, separate statistics which it predicts, we call that model **identified**. If the number of free parameters in a model is greater than the number of predicted statistics, we call it **underidentified**. The number of unknowns is greater than the number of knowns, and the model is of little use.

## References

Hoyle, R., ed. Handbook of Structural Equation Modeling

Lesson, J. Methodology for Genetic Studies: Identification of Models and Parameters

Retrieved from http://ibgwww.colorado.edu/twins2003/cdrom/HTML/BOOK/node84.htm on January 29, 2018

Zurbriggen, Eileen. Basics of Structural Equation Modeling

Retrieved from https://people.ucsc.edu/~zurbrigg/psy214b/09SEM3a.pdf on January 29, 2018

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