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I would also say that there is a definite anti-SAS attitude among some members of the R community (and S and S-Plus before R). This is unfortunate, because SAS is carefully developed under the direction of many top professional statisticians. It is well documented and its code is solid and reliable for what it does. There are definite reasons I prefer R to SAS myself, not the least of which is that SAS cannot quite escape some very old ruts. But I would like to encourage users to adopt a less theological attitude about statistical software.

I would also say that there is a definite anti-SAS attitude among some members of the R community (and S and S-Plus before R). This is unfortunate, because SAS is carefully developed under the direction of many top professional statisticians. It is well documented and its code is solid and reliable for what it does. There are definite reasons I prefer R to SAS myself, not the least of which is that SAS cannot quite escape some very old ruts. But I would like to encourage users to adopt a less tribal attitude about statistical software.

In the situation where you have data sampled from a population, then LS means or EMMs may very well be entirely inappropriate. They certainly don't estimate the marginal means of your population because the equal weighting is not appropriate. The emmeans* package provides various alternative weighting schemes, and some may be suited for a particular purpose; or not.

In the situation where you have data sampled from a population, then LS means or EMMs may very well be entirely inappropriate. They certainly don't estimate the marginal means of your population because the equal weighting is not appropriate. The emmeans package provides various alternative weighting schemes, and some may be suited for a particular purpose; or not.

Balanced experiments lie in very foundational places in statistics, including the writings of Fisher, Youden, Snedecor, Cochran, Cox, Box, and Tukey. But what if it isn't a balanced experiment? For example, a few observations were lost (completely at random). In very old design texts, what was suggested in some cases was the "method of unweighted means", whereby we use the values of $\bar Y_{ij.}$ and construct an analysis of those cell means as if they were data from a balanced experiment with $\tilde n$ observations per cell (where, typically, $\tilde n$ is the harmonic mean of the cell sample sizes). his is far preferable to just computing marginal means of the data, because some cells receive more weight than others, which can produce Simpson's-paradox-like effects.

Again, LS means are essentially the same idea as unweighted means, which is a very, very old idea. In LS means, we fit a model to the data and use it (in the two-way factorial case) to predict the $\mu_{ij}$, then our marginal means are estimated as equally-weighted marginal averages of these predictions, just as in unweighted-means analysis. But these LS means are linear functions of the model predictions, and hence of the regression coefficients; so they can be estimated from the model with no need for ad hoc quantities like $\tilde n$. The idea extends to other experimental designs, such as Latin squares, split-plots, etc., and even to covariance models (where typically we make predictions at the mean of each covariate). You can also generalize these ideas to experimental data analyzed with other types of models, including generalized linear models, ordinal models and multinomial models, zero-inflated models, etc. And the ideas can be applied to Bayesian models sitted via MCMC methods, simply by computing the relevant quantities from the posterior predictions.

In the situation where you have data sampled from a population, then LS means or EMMs may very well be entirely inappropriate. They certainly don't estimate the marginal means of your population because the equal weighting is not appropriate. the emmeans* package provides various alternative weighting schemes, and some may be suited for a particular purpose; or not.

What about type III sums of squares? What I would say is that you need to consider whether they are appropriate for an individual situation. SAS defines these in terms of estimable functions, and a given set of estimable functions corresponds to a family of contrasts that can usually be expressed as contrasts among LS means. If that family of contrasts is of interest, then the associated type III test is fine; and if not, it's not fine. And again, this has to do with the approriateness of the LS means being considered. I personally shy away from type III tests, but that is because I don't use omnibus tests for anything but model selection.

Balanced experiments lie in very foundational places in statistics, including the writings of Fisher, Youden, Snedecor, Cochran, Cox, Box, and Tukey. But what if it isn't a balanced experiment? For example, a few observations were lost (completely at random). In very old design texts, what was suggested in some cases was the "method of unweighted means", whereby we use the values of $\bar Y_{ij.}$ and construct an analysis of those cell means as if they were data from a balanced experiment with $\tilde n$ observations per cell (where, typically, $\tilde n$ is the harmonic mean of the cell sample sizes). This is far preferable to just computing marginal means of the data, because some cells receive more weight than others, which can produce Simpson's-paradox-like effects.

Again, LS means are essentially the same idea as unweighted means, which is a very, very old idea. In LS means, we fit a model to the data and use it (in the two-way factorial case) to predict the $\mu_{ij}$; then our marginal means are estimated as equally-weighted marginal averages of these predictions, just as in unweighted-means analysis. But these LS means are linear functions of the model predictions, and hence of the regression coefficients; so they can be estimated from the model with no need for ad hoc quantities like $\tilde n$. The idea extends to other experimental designs, such as Latin squares, split-plots, etc., and even to covariance models (where typically we make predictions at the mean of each covariate). You can also generalize these ideas to experimental data analyzed with other types of models, including generalized linear models, ordinal models and multinomial models, zero-inflated models, etc. And the ideas can be applied to Bayesian models fitted via MCMC methods, simply by computing the relevant quantities from the posterior predictions.

In the situation where you have data sampled from a population, then LS means or EMMs may very well be entirely inappropriate. They certainly don't estimate the marginal means of your population because the equal weighting is not appropriate. The emmeans* package provides various alternative weighting schemes, and some may be suited for a particular purpose; or not.

What about type III sums of squares? What I would say is that you need to consider whether they are appropriate for an individual situation. SAS defines these in terms of estimable functions, and a given set of estimable functions corresponds to a family of contrasts that can usually be expressed as contrasts among LS means. If that family of contrasts is of interest, then the associated type III test is fine; and if not, it's not fine. And again, this has to do with the appropriateness of the LS means being considered. I personally shy away from type III tests, but that is because I don't use omnibus tests for anything but model selection.