Hello, my question might be more theoretical. The datasets I currently analyse are not normally distributed (according to shapiro-wilk and kolgomorov-smirnov @ p = 0.05). Therefore, I prefer plotting them as boxplots. However, I would actually like to fit a nonlinear model (in that case a hill equation) to the (non-existing) mean in order to extract some parameters. So, is there any way and is it allowed to fit my function to the median instead of the mean values? I haven't found publications where this is done and I assume that this is for a good reason. I just don't know why and what else to do with my data.
Thanks for your help!
Philipp
read the attached link
https://statisticsbyjim.com/regression/curve-fitting-linear-nonlinear-regression/
There is nothing preventing you from fitting a relationship to the median values. You just need to remember that you are modelling the median of the distribution when you are interpreting the results.
we can use free statistical program to do statistical analysis.
I would suggest using Quantile Regression. You can choose the quantile value = 50, i.e. the median.
https://cran.r-project.org/web/packages/quantreg/quantreg.pdf
Barry Croke Thanks for your reply! If I get things right ordinary least squares (OLS) regression makes no assumption about the distribution of the data, thus as you said I could also fit my function to the median? Then taking the mean should also be fine, although it is more prone to outliers.
Milan Onderka I thought of using robust regression like the mean absolute deviation instead of OLS to reduce the effect of outliers.
In a related post Asit Kumar Batabyal suggested to use "median (as a measure of location) and median absolute deviation (as a measure of spread) instead of mean and standard deviation".
What do you think about this?
Outliers can have a significant impact on OLS regression because the least squares approach will the use of the squared residual puts a lot of emphasis on the points that have the largest residual as these will contribute strongly to the sum of squared residuals. This will tend to draw the regressed model away from where it should be. If this is a problem then you could use a different objective function (e.g. sum of absolute residuals).
All comes down to what you are trying to do, which is a bit hard to determine from what you have said so far. Normally, you would apply the regression to the data, but you are talking about taking the mean or median of the data. I assume this is for subsets of the data (e.g. binning the data along the x-axis), which you will then be using to generate a smaller set of data points for carrying out the regression.
Thanks for your replies! Barry Croke Good point about the weighting of squared residuals, I will consider a robust minimization routine instead!
Sorry if I was not specific enough. I attached the figure. Each data point is the weighted mean (+ propagated standard deviation) of three independent experiments (each with a distribution of N = approx. 1000 datapoints). Since the data are not normally distributed (which is no requirement for OLS) I was considering fitting the function to the median instead.
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