I have a dataset of growth response of a fungal mycelium to increasing doses of the fungicide. I have calculated linear model after log-transformation of the concentration values and i have tried to fit the data to 3-parameter log-logistic model in R program. How can I compare which model fits better to my data?
One aspect of how well a model fits the data is the error distribution (a model assumption).
The linear model on the log transformed outcome assumes normal error distribution on the log transformed outcome. If this is true the error is proportional to the outcome. But in some situations a log-linear relationship may exist while the error distribution is normal on the non-transformed scale.
You can investigate this by plotting the regression residuals against the fitted values. You may find that the error distribution is much closer to normal in one case.
An other aspect of how well the model fits the data is the deviance.
The deviance is lower if the model fits the data better, but a model that allows for non-linearity will almost always fit better than a linear one. Akaike's Information Criterion (AIC) and the Bayesian Information Criterion (BIC) are both available in R and they provide model goodness measures that penalise the more complex model. Both use the numbers of model parameters to measure model complexity.
If the model assumptions (linearity, error distribution etc.) are reasonably well met in case of both models you can choose the model with the lower AIC or BIC.
I guess, another option would be to plot both the observed and the fitted values for each model and see which one provides a better fit....
Residual plots (residuals versus fitted values or versus (log) dose are definitely helpful to check for linearity and variance homogeneity. I would add a QQ-plot (qqnorm()) for the residuals if the model assumes normally distributed errors. As I understand, the doses have been log-transformed. Proportionality of standard deviation and outcome is usually an issue, when the outcome is log-transformed.
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