week 3; Moderation Flashcards
ORDINAL/DISORDINAL
it is important to remember that a moderator may be associated with changing the strength of an IV-DV relationship (ordinal interaction), BUT it can also be associated with a change in the direction of the relationship (disordinal interaction). The change in direction may be gradual, ie have ranges across +ve and -ve etc
Sometimes there may be a strong positive relation at one end of the moderator scale, moving rightthough to a strongnegative relationship at the other extreme. In this situation may have 2 regions of slopes which are significant and areas in between which are not significant.
What is Moderation?
MODERATION is a hierarchical regression (an advanced Regression technique) which examines the moderating or interacting role, that a variable may play in the nature of the relationship b/n and IV and a DV (strength &/or direction), viathe introduction of an interaction term based on central variables. Where an interaction term is significant, simple slopes are examined which reflect the IV-DV relationship at different levels of the moderator.
Conscientiousness
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Perceived support»»»Grade
eg. As Perceived support increases, grades also increase, PLUS the effect of this is further increased as conscientiousness increases. (Mediation differs as it further explains why the DV relates to the IV in the first place.)
HIERARCHICAL REGRESSION
Hierarchical Regression uses non-independence of group observations, rather than considering everything simultaneously, by putting in something, finding out what it does, then putting in something else and seeing what it adds.
The “Hierarchical module” in spss does NOT do the correct Hierachical Regression. Spss will add in 1 variable at a time or blocks of them and tell a regression analysis, but the table will have multiple slabs reflecting what happens at each block (simultaneous effect of all variables). Each block is interpreted as adding whatever is in that block to whatever was in all the preceding blocks. BUT use PROCESS MACROS TO do a hierarchical or sequential model, you put a variable, or block of variables, in first and it will provide you with up-to-date data (unique contribution of variables entered as each step is computed). When you add further variables, the data updates to what is changing.
Multiplicative Moderation
There are a number of different types of moderation. The most common, seen in psychological examples, is the multiplicative moderation or simple moderation, where you have interaction between two variables and the effect of one variable is changed by the presence of another. The interaction happens between two quantitative variables. Whilst possible to have an interaction between a categorical and a quantitative variable in ordinary regression, it is better to analyse these using a different model.
The key processes that you need to go through for moderation (multiplicative) interactions–interactions between two quantitative (and quasi-continuous) variables, are as follows:
have a conceptual overview of interaction effects
centring the variables
computing the interaction term
entering predictors and interaction terms using hierarchical regression
interpreting SPSS output
plotting the interaction to aid interpretation.
An interaction is where the effect of one variable depends on the level of another. That is, the variables are not independent and so it is commonly referred to as the multiplicative interaction (literally multiplying two values together).
What is an Interaction?
INTERACTION
-the effect of 2 I/V’s is NOT independent
-the effect of an I/V depends upon the value of another I/V
eg being watched (I/V1) improves performance (D/V) for extroverts (IV2 high), BUT
being watched (I/V1) decreases performance (D/V) for introverts (I/V2 low).
-a common type of interaction in Regression is Multiplicative ie an “X” by “Y” interaction or
“X” x “Y”.
graph pics of interaction 3.3
Moderator effects have been plotted at levels of moderator for -1 SD, mean, and +1 SD. The Effect in the plots table output from macros PROCESS is how this was obtained then put numbers into excel template. The effect is a B VALUE (UNSTANDARDISED COEFFICIENT)
steps in checking for interactions
To test some of your independent variables for interactions, use this suggested four-step process:
Centre or standardise the variables you are going to use
Compute an interaction, which involves getting a mean and then possibly a standard deviation
Run the regression analysis
Consider the output. (This can involve a sneaky fifth step, which is to draw a picture of it. This can be useful because the output of interactions is really hard to do, and there are other programs that can do this for you such as PROCESS macro.)
models to describe the interaction
- Concept model eg
Z
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X……………………Y
- Regression model
eg X, Z and their product, predicts Y.
sample size
Possible suggestions include:
a) Your sample size needs to be 50, plus 8 times the number of variables involved. This is suggested as a good number to test whether multiple R (that is, an overall regression) is significant or not.
b) 104 variables plus the number of IVs, which is the correct number for testing the significance of an individual predictor. This is the minimum sample size—more cases are better. As you get very large samples, almost every correlation becomes significant.
power
Bootstrapping is a resampling procedure that uses data from one sample to generate a sampling distribution by repeatedly taking random samples from the known sample, with replacement. Bootstrap methods tend to be a little bit more efficient than other model-fitting methods. When people indicate that if you use the Process macro, you can get away with a smaller sample, that’s true up to a point. In the literature, you can find articles that do empirical power estimates. This works not by using theory, but by creating data, so you know:
what b is
what the standard deviations are
what the slopes and intercepts are.
The process works by generating random data and then pretending you don’t know what the data is. You analyse the data, and you see if you get the right answer back. By doing that, you can say, look, if there’s a significant effect there with a model that’s got these parameters, if I generate a random set of variables that has those parameters and then analyse those, how often do I get the right answer? You can build up a power model that way.
Often, this experiment will result in what psychologists regard as small to medium effects, around 300 cases, which can be detected quite reliably in this way. For larger effects, then often a sample size of 80–100 is sufficient.
calculating effect size
Remember, that we often talk about finding out how significant a relationship is. BUT in moderations or interactions etc, we really also want to know if an interaction is significant, and this is a bit more complex.
Effect size = fsquared
X and Z are predictors, and M is their interaction. ie use lower equation to determine effect size for the actual interaction . ie is interaction significant. Use the Cohen’s d value that you want as an effect size. Plug it into Gpower software and use the bottom, fuller equation looking at how significant is an interaction?, and Gpower will then say what sample size you need to see if you can then find the effect.
