Post on 21-Dec-2015
Quantitative Methods
Combining continuous and categorical variables
Combining categorical and continuous variables
Reprise of models fitted so far
YIELD=FERTILYIELDM=VARIETY
VOLUME=HEIGHTMATHS=ESSAYSSPECIES2=SPECIES1
AMA=YEARS+HGHTFINALHT=INITHT+WATER
WGHT=RLEG+LLEGPOETSAGE=BYEAR+DYEARLVOLUME=LDIAM+LHGHT
YIELD=BLOCK+BEANSEEDS=COLUMN+ROW+TREATMT
Combining categorical and continuous variables
Reprise of models fitted so far
YIELD=FERTILYIELDM=VARIETY
VOLUME=HEIGHTMATHS=ESSAYSSPECIES2=SPECIES1
AMA=YEARS+HGHTFINALHT=INITHT+WATER
WGHT=RLEG+LLEGPOETSAGE=BYEAR+DYEARLVOLUME=LDIAM+LHGHT
YIELD=BLOCK+BEANSEEDS=COLUMN+ROW+TREATMT
ANOVA table - whether x-variables predict y-variable
Coefficients table - how x-variables predict y-variable
Combining categorical and continuous variables
Model formulae, model and fitted values
Combining categorical and continuous variables
Model formulae, model and fitted values
Combining categorical and continuous variables
Model formulae, model and fitted values
Combining categorical and continuous variables
Model formulae, model and fitted values
BACAFTER = BACBEF+TREATMNT
TREATMNT Coef 1 1
BACAFTER = + BACBEF + 2 2 + 3 -1 -2
TREATMNT CoefPREDICTED 1 -1.590BACAFTER = -0.013 + 0.8831BACBEF + 2 -0.726 3 2.316
(Model Formula)
(Model)
(Fitted Value Equation or Best Fit Equation)
Combining categorical and continuous variables
Model formulae, model and fitted values
Combining categorical and continuous variables
Model formulae, model and fitted values
Combining categorical and continuous variables
Model formulae, model and fitted values
Combining categorical and continuous variables
Graphs and equations
Combining categorical and continuous variables
FAT = + *WEIGHT
FAT = + SEX Coeff M F -
FAT = + SEX Coeff + *WEIGHT M F -
Graphs and equations
Combining categorical and continuous variables
Graphs and equations
Combining categorical and continuous variables
Graphs and equations
Combining categorical and continuous variables
Orthogonality
… is a relationship that may hold between two x-variables
The general concept is that two x-variables are orthogonal if you can’t predict one when you know the other.
Combining categorical and continuous variables
Orthogonality
Combining categorical and continuous variables
Orthogonality
Combining categorical and continuous variables
Orthogonality
Combining categorical and continuous variables
Ambivalence
Combining categorical and continuous variables
Ambivalence
Combining categorical and continuous variables
Ambivalence
Combining categorical and continuous variables
Generality of GLM
Combining categorical and continuous variables
Last words…
Next week: Interactions - getting more complex
Read Chapter 7 (a long one)
• Continuous and categorical variables can be freely combined in a model formula
• Know how to construct the model• Know how to construct the fitted value equation• Some variables may be treated in either way• The GLM encompasses many traditional tests