Quantitative Methods Checking the models II: the other three assumptions.
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Transcript of Quantitative Methods Checking the models II: the other three assumptions.
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Quantitative Methods
Checking the models II:the other three assumptions
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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)
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Assumptions of GLM
TREATMNT Coef 1 1
BACAFTER = + BACBEF + 2 2 + 3 -1 -2(Model)
Checking the models II: the other 3 assumptions
![Page 4: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/4.jpg)
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
![Page 5: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/5.jpg)
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
![Page 6: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/6.jpg)
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
![Page 7: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/7.jpg)
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
![Page 8: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/8.jpg)
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
![Page 9: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/9.jpg)
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
![Page 10: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/10.jpg)
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
![Page 11: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/11.jpg)
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
![Page 12: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/12.jpg)
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
![Page 13: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/13.jpg)
Are the assumptions likely to be true?
Assumptions of GLM
IndependenceHomogeneity of varianceNormality of errorLinearity/additivity
Checking the models II: the other 3 assumptions
![Page 14: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/14.jpg)
Model Criticism
Checking the models II: the other 3 assumptions
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Model Criticism
Checking the models II: the other 3 assumptions
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Model Criticism
Checking the models II: the other 3 assumptions
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Transformations and Homogeneity
Checking the models II: the other 3 assumptions
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Transformations and Homogeneity
Checking the models II: the other 3 assumptions
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Transformations and Homogeneity
Checking the models II: the other 3 assumptions
![Page 20: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/20.jpg)
Transformations and Homogeneity
Checking the models II: the other 3 assumptions
![Page 21: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/21.jpg)
Transformations and Homogeneity
Checking the models II: the other 3 assumptions
![Page 22: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/22.jpg)
Transformations and Homogeneity
Checking the models II: the other 3 assumptions
![Page 23: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/23.jpg)
Transformations and Homogeneity
Checking the models II: the other 3 assumptions
![Page 24: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/24.jpg)
Transformations and Homogeneity
Checking the models II: the other 3 assumptions
None, or linearSquare rootLogNegative inverse
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Non-linearity
Checking the models II: the other 3 assumptions
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Non-linearity
Checking the models II: the other 3 assumptions
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Checking the models II: the other 3 assumptions
Non-linearity
![Page 28: Quantitative Methods Checking the models II: the other three assumptions.](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d365503460f94a0da80/html5/thumbnails/28.jpg)
Checking the models II: the other 3 assumptions
Non-linearity
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Example
Checking the models II: the other 3 assumptions
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Example
Checking the models II: the other 3 assumptions
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Example
Checking the models II: the other 3 assumptions
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Example
Checking the models II: the other 3 assumptions
MTB > let LOGDEN=log(DENSITY)
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Hints
Checking the models II: the other 3 assumptions
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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
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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)
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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