Quantitative Methods Checking the models I: independence.
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Quantitative Methods Checking the models I: independence
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Transcript of Quantitative Methods Checking the models I: independence.
Quantitative Methods
Checking the models I: independence
Checking the models I: independence
Assumptions of GLM
Checking the models I: independence
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)
Checking the models I: independence
Assumptions of GLM
BACAFTER = BACBEF+TREATMNT
TREATMNT Coef 1 1
BACAFTER = + BACBEF + 2 2 + 3 -1 -2
(Model Formula)
(Model)
Checking the models I: independence
Assumptions of GLM
TREATMNT Coef 1 1
BACAFTER = + BACBEF + 2 2 + 3 -1 -2(Model)
Checking the models I: independence
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 I: independence
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 I: independence
Independence in principle
Checking the models I: independence
Heterogeneous data
Checking the models I: independence
Heterogeneous data
Checking the models I: independence
Heterogeneous data
Checking the models I: independence
Heterogeneous data
Checking the models I: independence
Heterogeneous data
Checking the models I: independence
Heterogeneous data
Checking the models I: independence
Repeated measures
Checking the models I: independence
Repeated measures
Checking the models I: independence
Repeated measures
Checking the models I: independence
Repeated measures
Checking the models I: independence
Repeated measures
Single summary approach
Multivariate approach
Few summaries approach
Checking the models I: independence
Repeated measures
name C100 ’wtg’let wtg=LOGWT20-LOGWT3glm wtg=diet
LET K3=3-31/3 ! 31/3 is the average ofLET K8=8-31/3 ! 3, 8 and 20LET K20=20-31/3LET K1=K3**2+K8**2+K20**2LET RATE=(K3*LOGWT3+K8*LOGWT8+K20*LOGWT20)/K1
GLM RATE=DIET
Checking the models I: independence
Repeated measures
Checking the models I: independence
Repeated measures
GLM LOGWT60 RATE = DIET; MANOVA; NOUNIVARIATE.
Checking the models I: independence
Nested data
Checking the models I: independence
Nested data
Checking the models I: independence
Detecting non-independenceIn principle: would knowing the error for one or more
datapoints help you guess the error for some other datapoint?
Experiments: Does the datapoint correspond to the level of randomisation?
Observations: Are there groups of datapoints which are very likely to have similar residuals?
Be suspicious of
- Too many datapoints
- Implausible results
- Repeated measures
Checking the models I: independence
Last words…
• Independence is a key assumption, and is the most problematic in practice
• Always be alert to possible violations• Know what can be done at the analysis stage• Realise that mistakes at the design stage are
often unrecoverable at analysis
Checking the models II: the other three assumptions
Read Chapter 9
