Goodness of Fit Statistics: Comparing models

[x321]

I have some parameterised models and some data, I want to decide which of the models best represents the data. does anyone know if there's a statistic for this?

I did think about the Pearsons Xhi-squared coefficient at first but because the models have different numbers of freedom, the degrees of freedom will be different in each case, so I'm not sure I can compare the pearsons values to each other.

Any help appreciated.

 

[Ishuda]

I have some parameterised models and some data, I want to decide which of the models best represents the data. does anyone know if there's a statistic for this?

I did think about the Pearsons Xhi-squared coefficient at first but because the models have different numbers of freedom, the degrees of freedom will be different in each case, so I'm not sure I can compare the pearsons values to each other.

Any help appreciated.

In many cases just the residual sum of squares
s = \(\displaystyle \Sigma\, \epsilon_i^2\)
where \(\displaystyle \epsilon_i\) is the ith 'error' between fit and data and R² (sort of a normalized s) are used. See
http://en.wikipedia.org/wiki/Coefficient_of_determination
for example

Other tests can certainly be used. For example, see
http://en.wikipedia.org/wiki/Goodness_of_fit

 

[x321]

Thanks, the problem with using the residual sum of squares it that it doesn't take into account the degrees of freedom, as do those goodness-of-fit statistics on wiki. For example, a model with 10 optimised parameters will better fit the data than a model with 5 optimised parameters but I need a way to decide if the extra degrees parameters justify the gain. something like residual Xhi-square would work except that my data doesn't have a standard deviation for each point so I can't use that.

In many cases just the residual sum of squares
s = \(\displaystyle \Sigma\, \epsilon_i^2\)
where \(\displaystyle \epsilon_i\) is the ith 'error' between fit and data and R² (sort of a normalized s) are used. See
http://en.wikipedia.org/wiki/Coefficient_of_determination
for example

Other tests can certainly be used. For example, see
http://en.wikipedia.org/wiki/Goodness_of_fit