LXM K

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LXM K
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Some comparisons among groups and among time
periods can specified here. Others can be
specified in the syntax with the EMMEANS command
or the LMATRIX and MMATRIX commands.
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Other reference categories can be specified on
the CONTRAST command in syntax.
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Different combinations of marginal means can be
requested here. These generate EMMEANS commands
that can be altered to get additional comparisons.
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GLM dv1 dv2 dv3 dv4 BY group /WSFACTOR time
4 Polynomial /CONTRAST (group)Deviation
/METHOD SSTYPE(3) /EMMEANS TABLES(OVERALL)
/EMMEANS TABLES(group) COMPARE
ADJ(BONFERRONI) /EMMEANS TABLES(time) COMPARE
ADJ(BONFERRONI) /EMMEANS TABLES(grouptime)
compare(group) adj(bonferroni) /PRINT
DESCRIPTIVE PARAMETER TEST(SSCP) RSSCP
/CRITERIA ALPHA(.05) /WSDESIGN time
/DESIGN group .
This part was added in the syntax to get simple
effects of group within levels of time.
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The TIME effect indicates that there are
significant differences among the overall means
for the 4 dependent measures. The TIMEGROUP
effect indicates that some linear combination of
the 4 dependent variables provides significant
discrimination among the groups.
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The overall or averaged univariate test for the
repeated measures requires satisfying the
assumption of sphericity. When this assumption
is violated, three approaches can be used (a)
multivariate test (no sphericity assumption, but
assumes multivariate
normality) (b) single df tests (no sphericity
assumption, but assumes
prior expectations) (c) adjusted degrees of
freedom test (penalty for violation)
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These single df tests do not require the
sphericity assumption.
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Violating the sphericity assumption inflates the
Type I error rate. The degree of inflation
depends on the degree of violation. For our
example, a severe violation could lead to an
actual Type I error rate nearly double the
nominal rate. The severity of the violation is
indexed by epsilon, with values between 1/df1
(bad) and 1.00 (good).
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The p value when an F of 2.62 is tested under
different levels of sphericity violatation.
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The Greenhouse-Geisser and Huynh-Feldt
corrections each reduce the degrees of freedom
for the overall test, effectively increasing the
critical F against which the obtained F is
compared. The reduction in degrees of freedom is
proportional to the value of epsilon, which is
estimated slightly differently in the two
procedures. For this example, the full degrees of
freedom are df1 3 and df2 447. The critical
value for p .05 is 2.62. The adjusted df are
epsilondf1 and epsilondf2.
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The new critical value for testing significance.
Fcritical(3, 447) 2.62 Sphericity assumed
The Greenhouse-Geisser penalty.
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Averages across levels of Time
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A violation of sphericity can often be detected
here
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When sphericity if violated, the variances for
all possible difference scores will not be
homogeneous.
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GLM dv1 dv2 dv3 dv4 /WSFACTOR time 4
Polynomial /METHOD SSTYPE(3) /EMMEANS
TABLES(OVERALL) /EMMEANS TABLES(time)
/PRINT PARAMETER /CRITERIA ALPHA(.05)
/WSDESIGN time .
The spacing of the outcome measures matters and
needs to be properly specified. SPSS assumes
equally spaced measures.
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GLM dv1 dv2 dv3 dv4 /WSFACTOR time 4
Polynomial(1,2,6,12) /METHOD SSTYPE(3)
/EMMEANS TABLES(OVERALL) /EMMEANS
TABLES(time) /PRINT PARAMETER /CRITERIA
ALPHA(.05) /WSDESIGN time .
Unequal spacing is indicated in syntax
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These have not changed. Why not?
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But, these have changed because the spacing of
the measures is now different. The variance of
the means has been reallocated among the
polynomial effects.
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The repeated measures may have an experimental
structure to them. This structure can be
specified as part of the statistical design. It
could also be specified in the MMATRIX.
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These are the same as the multivariate tests. Why?
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The A x B x G interaction. What additional
follow-up tests could be conducted to determine
the nature of this interaction?
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GLM dv1 dv2 dv3 dv4 BY group /METHOD
SSTYPE(3) /mmatrix dv1 1 dv2 1 dv3 1 dv4 1
dv1 1 dv2 1 dv3 -1 dv4 -1 dv1
1 dv2 -1 dv3 1 dv4 -1 dv1 1 dv2 -1
dv3 -1 dv4 1 dv1 1 dv2 1 dv3 1 dv4
-3 /INTERCEPT INCLUDE /PRINT DESCRIPTIVE
PARAMETER /CRITERIA ALPHA(.05) /DESIGN
group .
The MMATRIX can be used when particular
comparisons among the dependent variables are
desired. In this case, no WSFACTOR command is
needed.
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Univariate tests
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These are the five comparisons specified on the
MMATRIX command. Because no LMATRIX was
specified, these transformations are collapsed
across groups. These are tests of the grand
means for the new linear combinations.
/mmatrix dv1 1 dv2 1 dv3 1 dv4 1
dv1 1 dv2 1 dv3 -1 dv4 -1 dv1 1
dv2 -1 dv3 1 dv4 -1 dv1 1 dv2 -1
dv3 -1 dv4 1 dv1 1 dv2 1 dv3 1
dv4 -3
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Significance tests for each MMATRIX
transformation.
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GLM dv1 dv2 dv3 dv4 BY group /METHOD
SSTYPE(3) /lmatrixgroup 1 0 0 0 0 -1
group 0 1 0 0 0 -1 group 0 0 1 0 0
-1 group 0 0 0 1 0 -1
group 0 0 0 0 1 -1 group 1 1 1 -1 -1
-1 /mmatrix dv1 1 dv2 1 dv3 1 dv4 1
dv1 1 dv2 1 dv3 -1 dv4 -1 dv1 1 dv2
-1 dv3 1 dv4 -1 dv1 1 dv2 -1 dv3 -1
dv4 1 dv1 1 dv2 1 dv3 1 dv4 -3
/INTERCEPT INCLUDE /PRINT DESCRIPTIVE
PARAMETER /CRITERIA ALPHA(.05)
Adding an LMATRIX requests that the new linear
combinations from the MMATRIX be compared
according to the codes in the LMATRIX
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compute sum dv1dv2dv3dv4 . compute
cdv1dv2-dv3-dv4 . compute ddv1-dv2dv3-dv4
. compute c_by_ddv1-dv2-dv3dv4 . EXECUTE .
Repeated measures designs can be analyzed in
multiple regression. The trick is realize that
the MMATRIX creates new dependent variables and
each one needs to be analyzed separately.
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REGRESSION /MISSING LISTWISE /STATISTICS
COEFF OUTS R ANOVA /CRITERIAPIN(.05)
POUT(.10) /NOORIGIN /DEPENDENT sum
/METHODENTER d1 d2 d3 d4 d5 .
What part of the original repeated measures
analysis will this produce?
compute sum dv1dv2dv3dv4 . compute
cdv1dv2-dv3-dv4 . compute ddv1-dv2dv3-dv4
. compute c_by_ddv1-dv2-dv3dv4 .
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REGRESSION /MISSING LISTWISE /STATISTICS
COEFF OUTS R ANOVA /CRITERIAPIN(.05)
POUT(.10) /NOORIGIN /DEPENDENT c
/METHODENTER d1 d2 d3 d4 d5 .
This one?
compute sum dv1dv2dv3dv4 . compute
cdv1dv2-dv3-dv4 . compute ddv1-dv2dv3-dv4
. compute c_by_ddv1-dv2-dv3dv4 .
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REGRESSION /MISSING LISTWISE /STATISTICS
COEFF OUTS R ANOVA /CRITERIAPIN(.05)
POUT(.10) /NOORIGIN /DEPENDENT d
/METHODENTER d1 d2 d3 d4 d5 . REGRESSION
/MISSING LISTWISE /STATISTICS COEFF OUTS R
ANOVA /CRITERIAPIN(.05) POUT(.10) /NOORIGIN
/DEPENDENT c_by_d /METHODENTER d1 d2 d3 d4 d5
.
compute sum dv1dv2dv3dv4 . compute
cdv1dv2-dv3-dv4 . compute ddv1-dv2dv3-dv4
. compute c_by_ddv1-dv2-dv3dv4 .
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GLM dv1 dv2 dv3 dv4 BY a b /WSFACTOR g 2 h
2 /METHOD SSTYPE(3) /EMMEANS
TABLES(abgh) compare(a) /EMMEANS
TABLES(abgh) compare(b) /EMMEANS
TABLES(abgh) compare(g) /EMMEANS
TABLES(abgh) compare(h) /PRINT DESCRIPTIVE
PARAMETER /CRITERIA ALPHA(.05) /WSDESIGN
g h gh /DESIGN a b ab .
When there are significant interactions, they can
be further investigated in several ways. Here
the simple (simple, simple) main effects are
requested.
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GLM dv1 dv2 dv3 dv4 BY group /METHOD
SSTYPE(3) /lmatrixgroup 1 -1 -1 1 0 0 group 1
1 1 1 -2 -2 /PRINT DESCRIPTIVE PARAMETER
/CRITERIA ALPHA(.05) /DESIGN group .
Other simple effects can be specified in syntax
using the LMATRIX, the MMATRIX, or both. Here
the simple effects of A within levels of G and H.
Because no WSFACTOR command is requested, each
contrast on the LMATRIX command will be examined
for each DV separately (i.e., within levels of G
and H).
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LXM K OK?