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Quantitative Methods Checking the models II: the other three assumptions
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Quantitative Methods
Checking the models II:the other three assumptions
Checking the models II: the other 3 assumptions
Assumptions of GLM
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)
Assumptions of GLM
TREATMNT Coef 1 1
BACAFTER = + BACBEF + 2 2 + 3 -1 -2(Model)
Checking the models II: the other 3 assumptions
Assumptions of GLM
TREATMNT Coef 1 1
BACAFTER = + BACBEF + 2 2 + 3 -1 -2(Model)
Assumptions of GLM
IndependenceHomogeneity of varianceNormality of errorLinearity/additivity
Checking the models II: the other 3 assumptions
Assumptions of GLM
TREATMNT Coef 1 1
BACAFTER = + BACBEF + 2 2 + 3 -1 -2(Model)
Assumptions of GLM
IndependenceHomogeneity of varianceNormality of errorLinearity/additivity
Checking the models II: the other 3 assumptions
Assumptions of GLM
TREATMNT Coef 1 1
BACAFTER = + BACBEF + 2 2 + 3 -1 -2(Model)
Assumptions of GLM
IndependenceHomogeneity of varianceNormality of errorLinearity/additivity
Checking the models II: the other 3 assumptions
Assumptions of GLM
TREATMNT Coef 1 1
BACAFTER = + BACBEF + 2 2 + 3 -1 -2(Model)
Assumptions of GLM
IndependenceHomogeneity of varianceNormality of errorLinearity/additivity
Checking the models II: the other 3 assumptions
Assumptions of GLM
TREATMNT Coef 1 1
BACAFTER = + BACBEF + 2 2 + 3 -1 -2(Model)
Assumptions of GLM
IndependenceHomogeneity of varianceNormality of errorLinearity/additivity
Checking the models II: the other 3 assumptions
Assumptions of GLM
TREATMNT Coef 1 1
BACAFTER = + BACBEF + 2 2 + 3 -1 -2(Model)
Assumptions of GLM
IndependenceHomogeneity of varianceNormality of errorLinearity/additivity
Checking the models II: the other 3 assumptions
Assumptions of GLM
TREATMNT Coef 1 1
BACAFTER = + BACBEF + 2 2 + 3 -1 -2(Model)
Assumptions of GLM
IndependenceHomogeneity of varianceNormality of errorLinearity/additivity
Checking the models II: the other 3 assumptions
Assumptions of GLM
TREATMNT Coef 1 1
BACAFTER = + BACBEF + 2 2 + 3 -1 -2(Model)
Assumptions of GLM
IndependenceHomogeneity of varianceNormality of errorLinearity/additivity
Checking the models II: the other 3 assumptions
Assumptions of GLM
TREATMNT Coef 1 1
BACAFTER = + BACBEF + 2 2 + 3 -1 -2(Model)
Assumptions of GLM
IndependenceHomogeneity of varianceNormality of errorLinearity/additivity
Checking the models II: the other 3 assumptions
Are the assumptions likely to be true?
Assumptions of GLM
IndependenceHomogeneity of varianceNormality of errorLinearity/additivity
Checking the models II: the other 3 assumptions
Model Criticism
Checking the models II: the other 3 assumptions
Model Criticism
Checking the models II: the other 3 assumptions
Model Criticism
Checking the models II: the other 3 assumptions
Transformations and Homogeneity
Checking the models II: the other 3 assumptions
Transformations and Homogeneity
Checking the models II: the other 3 assumptions
Transformations and Homogeneity
Checking the models II: the other 3 assumptions
Transformations and Homogeneity
Checking the models II: the other 3 assumptions
Transformations and Homogeneity
Checking the models II: the other 3 assumptions
Transformations and Homogeneity
Checking the models II: the other 3 assumptions
Transformations and Homogeneity
Checking the models II: the other 3 assumptions
Transformations and Homogeneity
Checking the models II: the other 3 assumptions
None, or linearSquare rootLogNegative inverse
Non-linearity
Checking the models II: the other 3 assumptions
Non-linearity
Checking the models II: the other 3 assumptions
Checking the models II: the other 3 assumptions
Non-linearity
Checking the models II: the other 3 assumptions
Non-linearity
Example
Checking the models II: the other 3 assumptions
Example
Checking the models II: the other 3 assumptions
Example
Checking the models II: the other 3 assumptions
Example
Checking the models II: the other 3 assumptions
MTB > let LOGDEN=log(DENSITY)
Hints
Checking the models II: the other 3 assumptions
Hints
Checking the models II: the other 3 assumptions
Morphometric data: logCount data: square rootProportional data: angularSurvival data: negative inverse
Don’t be too picky
Selecting a transformation
Checking the models II: the other 3 assumptions
With covariates, consider transforming X too
Continuous y-variable - varying strengths Increasing strength: none, square root, log, negative inverse
Proportions - root arcsin
Counts - square root
Based on homogenising the error variance
Go through the model criticism process again (and if necessary again and again)
Last words…
• You should always check assumptions as much as you can using the techniques of model criticism
• Transformations can help to ‘cure’ failures to meet assumptions
• Always repeat model criticism after transforming• Homogeneity of variance is the priority for
transformations
Model selection I: principles of model choice and designed experiments
Read Chapter 10
Checking the models II: the other 3 assumptions
