quantitative methods checking the models ii: the other three assumptions

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