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By Christopher F. Baum

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By default, the model will include an intercept term, unless it is suppressed by a ‘-1’ in the formula. The second argument to lm supplies a data frame, within which the variables in the formula can be found. The terms on the right hand side of the model formula specify how the model matrix, X, is to be specified. In fact, in this example, the terms give the model matrix columns directly. 30 Scale−Location plot Standardized residuals 0 Theoretical Quantiles 100 200 300 400 500 2 Fitted values 4 6 8 10 12 14 Obs.

Comp1) The first argument to lm is a model formula, specifying the structure of the model to be fitted. partner. By default, the model will include an intercept term, unless it is suppressed by a ‘-1’ in the formula. The second argument to lm supplies a data frame, within which the variables in the formula can be found. The terms on the right hand side of the model formula specify how the model matrix, X, is to be specified. In fact, in this example, the terms give the model matrix columns directly.

There are of course many ways of constraining this model to achieve identifiability. One possibility (the default in R) is to set β0 = γ0 = δ00 = δ01 = δ10 = δ20 = 0. The resulting model can still produce any fitted value vector that the full model can produce, but all the columns of its model matrix are independent, so that the model is identifiable: PRACTICAL MODELLING WITH FACTORS 41    1 0 0 0 0 0 µ1  µ2   1 0 0 0 0 0        α  µ3   1 0 0 1 0 0        µ4   1 1 0 1 1 0   β1       β2   µ5  =  1 1 0 1 1 0   .

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