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General Linear Model General Linear Model

General Linear Model - PowerPoint Presentation

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General Linear Model - PPT Presentation

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

correlation regression linear model regression correlation model linear analysis variables error random normality bivariate group general variable assumptions fixed

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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)