Psyc 340 Chapter 8

what doe researchers want when they use it?

A researcher wants to determine whether particular predictors can account for unique variance in the outcome variable with the effects of other predictor variables statistically removed.

Multiple regression coefficient

R, describes the degree of relationship between the criterion variable (y) and the set of predictor variables (x's). Expresses the usefulness of a regression equation for predicting a criterion variable

Fit index

indicates how well the hypothesized model fits the data.

A variable that correlates with a factor is said to ______. Usually have to load at least - or + ____

load on that factor .30

Factor matrix

presents the solution to a factor analysis

Special opportunity with nested data

the ability for researchers to study variables that operate at different levels of analysis

Cross-lagged panel correlation design- define and give example

the correlation between two variables, x and y, is calculated at two different points in time. Then correlations are calculated between measurements of the two variables across time. Ex: x at time 1 with y at time 2. And y at time 1 with x at time 2.

Path analysis

refers to structural equations in which single measures of each construct are used

β1

slope of line

A multiple correlation coefficient can be _____ to show the percentage of variance in the criterion variable (y) that can be accounted for by the set of predictor variables

squared

Latent variable processing

structural equation modeling in which each construct in the model is assessed by two or more measures

If x causes y, then we should find that ____

the correlation between x at time 1 and y at time 2 is larger than the correlation between y at time 1 and x at time 2

Structural modeling mathematically compares the ____ to _____

the correlation matrix implied by a particular hypothesized model to the real correlation matrix based on the data that we collect

Latent variable processing helps get rid of _____

the measurement error of any single measure

Factor loadings

the numerical entries in a factor matrix. They are the correlations of the variables with the factors

Structural equation modeling gives us information regarding______

the plausibility of causal hypotheses

Hierarchical multiple regression

the predictor variables are entered into the equation in an order that is predetermined by the researcher based on hypotheses that he or she wants to test

β0

the regression constant. Y-intercept

Problem with nested designs

the responses of the participants within any particular group are not independent of one another

Latent variables

the underlying factors that cause variables to correlate with one another

Two common uses of hierarchical multiple regression are:

to eliminate confounding variables and to test mediational hypotheses

Multilevel modeling

use with nested data. Deals with the problem of nonindependence of participants' responses within each nested group. Allows us to tease apart the various influences on a construct by analyzing variables operating at all levels of the nested structure simultaneously. It also allows us to see how variables at one level are influenced by variables on another level.

Confounded variables

variables that tend to occur together, making their distinct effects on behavior difficult to separate

Factor analysis identifies and expresses the factor structure by using mathematical procedures rather than by eyeballing the data

...

R ranges from___ to ____

.00 to 1.00

We compare fit indices for different models to see____

which one fits the data best

See page 177

...

Stepwise process stops when one of two things happen:

1. All will be used because they all make a unique contribution to the prediction of the criterion variable 2. Only some are in equation, but the rest can't predict anything uniquely

The four advanced correlational methods this chapter covers allow researchers to: (4)

1. Develop equations that describe how variables are related and that allows us to predict one variable from one or more variables (regression analysis) 2. Explore the likely direction of causality between two or more variables that are correlated (cross-lagged panel and structural equations analysis) 3. Examine relationships among variables that are measured at different levels of analysis (multilevel modeling) 4. Identify basic dimensions that underlie sets of correlations (factor analysis)

These equations allow us to do two things:

1. Have a mathematical description of how the variables are related 2. Predict one variable from others

Three primary types of multiple regression procedures:

1. Standard 2. Stepwise 3. Hierarchical

Factor analysis has three basic uses:

1. Study the underlying structure of psychological constructs 2. Reduce a large number of variables to a smaller, more manageable set of data 3. Used in the development of self-report measures of attitudes and personality

_____ occur when the effect of x on y occurs because of an intervening variable, z (example, amount of mental chatter mediates effect of yoga on stress level)

Mediation effects

steps 1 and 2

Step 1: put in variable that correlates highest Step 2: put in variable that correlates highest with first variable in there. Look for unique variance, not variance that is already accounted for

The predictor variable - symbol and define

x - the variable we are using to predict y

regression line formula

y = β0 + β1 x

Factor analysis

a class of statistical techniques that are used to analyze the interrelationships among a large number of variables.

Structural equations modeling-

a more sophisticated way to test causal hypotheses from correlational data. Given the pattern of correlations among a set of variables, certain causal explanations of the relationships among the variables are more logical or likely than others. The researcher makes precise predictions regarding how three or more variables are causally related. Each model implies that the variables should be correlated in particular way.

The goal of regression analysis is to develop _____

a regression equation, the equation for the line that best fits the pattern of the data

Regression equation

allows us to predict scores on one variable on the basis of scores on one or more other variables

Dependent variable in regression equation - also called and define

also called criterion or outcome variable. The variable we want to predict

Standard multiple regression- also called and define

also called simultaneous multiple regression. All of the predictor variables are entered into the regression analysis at the same time. The equation has a regression constant and separate regression coefficients for each predictor

Stepwise multiple regression

builds the regression equation by entering the predictor variables one at a time

Nested data

data that are in groups. For example, children from a classroom are nested together, as are the children in a certain school

Regression analyses allow us to_____

develop equations that describe precisely how those variables relate to that response

Multiple regression analysis

develops regression equations that include more than one predictor

Regression analyses are often used to ______

extend the findings of correlational research

The purpose of factor analysis is to ______

identify the underlying dimensions or factors that account for the relationships that are observed among variables