Hello,
I have a linear model (both with categorical factors and covariates) with a continuous response variable. I know that the observed means can be different from least square means based on the model, so I was wondering whether it is appropriate to create plots (e.g. boxplots that compare means from different factor categories) based on the observed means or if one should build them based on the least square means. Also, when presenting the results in the results section of a paper, should one present the least square means or is it still appropriate to present the observed means?
Thank you.
By "least squares means," are you indicating each predicted y-value, given certain values for your other variables, and by "observed means," are you referring to the mean of the y-variable data? If so, these are "apples and oranges," i.e., not the same. So what you use will depend on what you want to do with it.
Think of the former above as the value for y on a regression line (straight or curved) for any point along that line. It is not the same as averaging the y-values.
Don't forget that heteroscedasticity is to be expected. This is natural any time one predicted-y value is different from another. (See Brewer, K.R.W.(2002), Combined Survey Sampling Inference: Weighing Basu's Elephants, Arnold: London and Oxford University Press, mid-page 111.)
the method of least squares is used to find the linear model of two variables.
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