Instructional Materials http coreecuedupsycwuenschkPPPPMultReghtm aka httptinyurlcommultreg4u Introducing the General Linear Models As noted by the General the GLM can be used to relate one set of things ID: 384681
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Slide1
General Linear ModelSlide2
Instructional Materials
http://core.ecu.edu/psyc/wuenschk/PP/PP-MultReg.htm
aka
,
http://tinyurl.com/multreg4uSlide3
Introducing the GeneralSlide4
Linear Models
As noted by the General, the GLM can be used to relate one set of things (Ys
) to another set of things (X).
It can also be used with only one set of things.Slide5
Bivariate Linear Function
Y = a +
bX
+ error
This is probably what you have in mind when thinking of a linear model.
Spatially, it is represented in two-dimensional (Cartesian) space.Slide6
Least Squares Criterion
Linear models produce parameter estimates (intercepts and slopes) such that the sum of squared deviations between Y and predicted Y is minimized.Slide7
Univariate Regression
The mean is a
univariate
least squares predictor.
The prediction model is
The sum of the squared deviations between Y and mean Y is smaller than that for any reference value of Y. Slide8
Fixed and Random Variables
A FIXED variable is one for which you have every possible value of interest in your sample.Example: Subject sex, female or male.A RANDOM variable is one where the sample values are randomly obtained from the population of values.
Example: Height of subject.Slide9
Correlation & Regression
If Y is random and X is fixed, the model is a regression model.If both Y and X are random, the model is a correlation model.
Researchers
generally
think that
Correlation
= compute the
corr
coeff
,
r
Regression = find an equation to predict Y from XSlide10
Assumptions, Bivariate Correlation
Homoscedasticity across Y|X
Normality of Y|X
Normality of Y ignoring X
Homoscedasticity across X|Y
Normality of X|Y
Normality of X ignoring Y
The first three should look familiar,
you make
them with the pooled variances
t
.Slide11
Bivariate NormalSlide12
When Do Assumptions Apply?
Only when employing t or F
.
That is, obtaining a
p
value
or constructing a confidence interval
.
With regression analysis, only the first three assumptions (regarding Y) are made.Slide13
Sources of Error
Y = a + bX + errorError
in the measurement of X and or Y or in the manipulation of X.
The influence upon Y of variables other than X (extraneous variables), including variables that interact with X.
Any nonlinear influence of X upon Y.Slide14
The Regression Line
r2 < 1
Predicted Y regresses towards mean Y
In
univariate
regression, it regresses all the way to the mean for every case.Slide15
Uses of Correlation/Regression
Analysis
Measure the degree of linear association
Correlation
does
imply causation
Necessary but not sufficient
Third variable problems
Reliability
Validity
Independent Samples
t
– point
biserial
r
Y = a + b
Group (Group is 0 or 1)Slide16
Uses of Correlation/Regression Analysis
Contingency tables --
Rows =
a
+
b
Columns
Multiple correlation/regressionSlide17
Uses of Correlation/Regression Analysis
Analysis of variance (ANOVA)
PolitConserv
=
a
+
b
1
Republican? +
b
2
Democrat?
k
= 3, the third group is all othersSlide18
Uses of Correlation/Regression Analysis
Canonical correlation/regression
(homophobia, homo-aggression) =
(psychopathic deviance, masculinity, hypomania, clinical defensiveness)
High
homonegativity
= hypomanic, unusually frank, stereotypically masculine, psychopathically deviant (antisocial)