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General Linear Models - 1 (ANOVA (extended to incorp continuous expl va.…
General Linear Models - 1
ANOVA
extended to incorp
continuous expl va. = ANCOVA
able to be formulated using a
linear regression model
categorical explanatory va.
methodological problems if
large diff in sample size
(ie unbalanced designs)
test for differences in means
between >2 groups
regression models able to deal
with unequal samples sizes
Categorical explanatory va's.
For
cont
va's - regression co-eff. (b):
the outcome is predicted to change
by x for each unit increase in the indep va.
For 2 categories:
the outcome changes by x when
you move from 1st to 2nd category
For >2 categories:
the outcome changes by x when
you move from 1st to 2nd cat,
from 2nd to 3rd cat etc
Problem is change in outcome
btwn categories is not linear or
no real order for categories
Dummy variables
Binary: 0 or 1
0 - referent
simple coding system -
allows each category to have own
regression coeff & prediction
For va with
m
categories
need
m-1
dummy va
so each cat is unique
combo of dummy va's.
D1, D2, D3 etc
Specify model:
Outcome (cont va) =
β - difference in predicted ex time
btwn under &
overweight
β - difference in predicted ex time
btwn normal &
overweight
β - slope - coeff attached to HR,
change in ex time per beat of HR
To compare to
normal weight
need to change referent group
(re-allocate dummy va's & repeat)
β - y intercept - value when all X are 0
predicted exercise time when all va are 0
Allocate dummy variables