Quantitative Methods Combining continuous and categorical variables.
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Transcript of Quantitative Methods Combining continuous and categorical variables.
![Page 1: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/1.jpg)
Quantitative Methods
Combining continuous and categorical variables
![Page 2: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/2.jpg)
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
![Page 3: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/3.jpg)
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
![Page 4: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/4.jpg)
Combining categorical and continuous variables
Model formulae, model and fitted values
![Page 5: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/5.jpg)
Combining categorical and continuous variables
Model formulae, model and fitted values
![Page 6: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/6.jpg)
Combining categorical and continuous variables
Model formulae, model and fitted values
![Page 7: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/7.jpg)
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)
![Page 8: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/8.jpg)
Combining categorical and continuous variables
Model formulae, model and fitted values
![Page 9: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/9.jpg)
Combining categorical and continuous variables
Model formulae, model and fitted values
![Page 10: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/10.jpg)
Combining categorical and continuous variables
Model formulae, model and fitted values
![Page 11: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/11.jpg)
Combining categorical and continuous variables
Graphs and equations
![Page 12: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/12.jpg)
Combining categorical and continuous variables
FAT = + *WEIGHT
FAT = + SEX Coeff M F -
FAT = + SEX Coeff + *WEIGHT M F -
Graphs and equations
![Page 13: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/13.jpg)
Combining categorical and continuous variables
Graphs and equations
![Page 14: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/14.jpg)
Combining categorical and continuous variables
Graphs and equations
![Page 15: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/15.jpg)
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.
![Page 16: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/16.jpg)
Combining categorical and continuous variables
Orthogonality
![Page 17: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/17.jpg)
Combining categorical and continuous variables
Orthogonality
![Page 18: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/18.jpg)
Combining categorical and continuous variables
Orthogonality
![Page 19: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/19.jpg)
Combining categorical and continuous variables
Ambivalence
![Page 20: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/20.jpg)
Combining categorical and continuous variables
Ambivalence
![Page 21: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/21.jpg)
Combining categorical and continuous variables
Ambivalence
![Page 22: Quantitative Methods Combining continuous and categorical variables.](https://reader038.fdocuments.us/reader038/viewer/2022110207/56649d6a5503460f94a48dad/html5/thumbnails/22.jpg)
Combining categorical and continuous variables
Generality of GLM
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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