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  2.  
  3. Maastricht University (UM)
  4.  
  5. PSY4107 Advanced Statistics II

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AdvStatIISummary

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 15 keer verkocht
  • Vak
  • PSY4107 Advanced Statistics II
  • Instelling
  • Maastricht University (UM)

Summary of my notes on the lectures, practical lectures, formative tests and key points for each task. The notes on the practical lectures contain answers and the tables from the SPSS output where it was necessary and the formative test includes how got to the solutions. Naturally, this is just a ...

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Document informatie

  • 29 mei 2017
  • 192
  • 2016/2017
  • Samenvatting

Onderwerpen

  • statistics
  • advanced statistics
  • rma
  • ii
  • summary

Geschreven voor

  • Maastricht University (UM)
  • Cognitive Neuroscience Research Master
  • PSY4107 Advanced Statistics II
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Voorbeeld van de inhoud

PSY4107 –
Advanced
Statistics II
RMA Cognitive and Clinical Science Period 3
(Maastricht University)
This course focuses on repeated measures designs and starts with a review of oneway and
twoway within-subject designs, and split-plot designs with a covariate. This review is
followed by a treatment of mixed (multilevel) linear regression for nested and longitudinal
designs. We will start this treatment with so-called marginal models for repeated measures
as a flexible alternative to repeated measures ANOVA in case of missing data or within-
subject covariates, and end with random effects models for repeated measures and nested
designs. Part II concludes with the topic of optimal design and sample size.




This is a personal summary of this course. Therefore, this summary may contain errors and does
not replace the knowledge a student should acquire throughout this course.



February 2017

, Table of Content
Topic 1 - Oneway within-subject ANOVA ............................................................................................. 3
Lecture 1 .............................................................................................................................................. 3
Practical Lecture 1 ............................................................................................................................. 13
Meeting 1........................................................................................................................................... 20
2010 ............................................................................................................................................... 20
2011 ............................................................................................................................................... 21
2012 ............................................................................................................................................... 22
Topic 2 - Twoway WS ANOVA and split-plot (BS*WS) ANOVA ..................................................... 24
Lecture 2 ............................................................................................................................................ 24
Practical Lecture 2 ............................................................................................................................. 38
Meeting 2........................................................................................................................................... 47
2010 ............................................................................................................................................... 47
2011 ............................................................................................................................................... 49
2012 ............................................................................................................................................... 51
Topic 3 - Covariates in WS and split-plot ANOVA.............................................................................. 55
Lecture 3 ............................................................................................................................................ 55
Practical Lecture 3 ............................................................................................................................. 67
Meeting 3........................................................................................................................................... 75
2010 ............................................................................................................................................... 75
2011 ............................................................................................................................................... 76
2012 ............................................................................................................................................... 78
Topic 4 - Mixed (multilevel) regression for longitudinal data: marginal models ................................. 79
Lecture 4 ............................................................................................................................................ 79
Practical Lecture 4 ............................................................................................................................. 92
Meeting 4......................................................................................................................................... 101
2010 ............................................................................................................................................. 101
2011 ............................................................................................................................................. 104
Topic 5 - Mixed regression for longitudinal and nested data: random intercept ................................. 106
Lecture 5 .......................................................................................................................................... 106
Practical Lecture 5 ........................................................................................................................... 121
Meeting 5......................................................................................................................................... 129
2010 ............................................................................................................................................. 129
2011 ............................................................................................................................................. 130
Topic 6 - Mixed regression for longitudinal and nested data: random slope ...................................... 133
Lecture 6 .......................................................................................................................................... 133



1

, Practical Lecture 6 ........................................................................................................................... 146
Meeting 6......................................................................................................................................... 158
2012 ............................................................................................................................................. 158
Topic 7 - Optimal design, sample size ................................................................................................ 163
Lecture 7 .......................................................................................................................................... 163
Practical Lecture 7 ........................................................................................................................... 175
Meeting 7......................................................................................................................................... 181
2010 ............................................................................................................................................. 181
2011 ............................................................................................................................................. 182
2012 ............................................................................................................................................. 183
Task Notes ........................................................................................................................................... 185
Appendix: Chi square values ............................................................................................................... 191




2

,Topic 1 - Oneway within-subject ANOVA
Lecture 1
 What is a WS design?
o K repeated measures of a (quantitative) outcome Y
o On the same N persons (or animals, families etc.)
o under K conditions or at K time points
 Types of WS design
o WS exp, replications blocked, crossover




 N = 40 students
 K= 4 conditions (stand, rest, bonus, rest+bonus)
 192 trials per conditions, presented in blocked order
 condition order counterbalanced BS (Latin square)
 outcome: mean RT
(per set of 6 trials, 32 sets per person per condition)




o WS exp, replications mixed, event-related design




 N = 12 students
 K = 4 angles of rotation (x same/different)
 32 trials per angle (16 same, 16 diff), mixed
 outcome: mean RT of all 32 trials
(per person per angle)




3

, o observational studies: growth curves (VGT – Progress test)




o repeated measures in BS exp (BS*WS = split-plot)
 Within-subject versus between-subject:
o Advantages and drawbacks
 Advantages:
 much smaller N of persons needed
 each person is his/her own control
 Drawbacks:
 not feasible in case of irreversible treatment effect
 risk of „carry over„ effects (wash-out needed)
o Sample size
 For comparing two conditions on a quantitative Y:
 BS: unpaired t-test (or 1-way BS ANOVA)
 WS: paired t-test (or 1-way WS ANOVA)
 Due to smaller residual outcome variance, and observing
each subject in each condition, WS needs only (1-ρ)/2 × total
sample size of BS, where ρ = correlation between paired
samples
o Reduced SS(error)




4

, Univariate method




o The model




o Estimation




 If only 1 observation: you cannot separate interaction
 Interaction effect = (Yij –Yi – Yj + Ytotal)
 With only 1 observation interaction effect and residual is same
o Example: raw data




o Example: SS(total)

Sum of squares
(-3)2 + (-1)2 = 10

Individual score (Yij) – Grand mean (Y)
6 – 10 = -4




5

,o Example: SS(condition)




 Condition mean (Yj) – Grand mean (Y)
 8 – 10 = -2
o Example: SS (person)




 Person mean (Yi) – Grand mean (Y)
 8 – 10 = -2
o Example: SS(residual)




 Individual score (Yij) – Person/ Condition marginal mean
 7–8=1
o Testing



 Dividing by df gives the MS‟s for F-test, but:
Only 1 observation per cell (= person x condition
→ Interaction + error cannot be separated, MS(residual) is a
mix of interaction and error!
 And person is random, not fixed → affects E(MS)
 So what is the corrected F-test then?




6

, o Denominator of F




 1-way WS design: treat fixed, person random, so:
 if > 1 repli: test treat effect against interaction
 if = 1 repli: test treat effect against residual (error+interaction pooled)
 then: person and person*treat effects untestable. But who
wants to test these anyway?
(There would only be one time point at which person is tested
and to differentiate person effect and person*treatment effect
you would need at least 2 different time points)
→“You don’t have to understand the details, just believe it”
 choice of denominator of F follows from the E(MS) table for that design
 ANOVA of raw RTs ( > 1 replications per cell) gives the same F and p for the
condition effect as does ANOVA of average RT across trials !
 in example: F= MS(cond) / MS(resid) = .67
o Sphericity
 assumption: sphericity
= each pairwise difference has same variance
→ each pairwise comparison same SE (= SD / √n)
≈ compound symmetry: same variance in each condition, same
correlation in all pairs of conditions
 Problem: Rarely valid if K > 2 conditions
 larger type I error risk for F-test
 too small / too large SE‟s for pairwise comparisons (higher risk of TI
errors for some and TII for others)
 Solutions:
 Epsilon-adjustment of df in univariate ANOVA:
o Multiply df(numerator) and df(denominator) with a factor
epsilon (ε) < 1
→ critical F-value higher
 lower-bound ε = 1/(K-1) , is an overcorrection
(overcorrection more extreme with more conditions)
 Better: GG (or HF) , ε lower (critical F higher) as
sphericity is more strongly violated.
 “You do not have to know how it is computed”
 multivariate ANOVA
 From SUMMARY OF LECTURE


7

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