Moderation, Logistic Regression, Mixed ANOVA Flashcards

1
Q

What kind of relationship do we look for in a moderator

A

Is the relationship between predictor (X) and outcome (Y) affected by the moderator (M).

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2
Q

What are 4 different changes in relationship with a moderator

A

1.smaller
2.larger
3.disappears
4.direction changes

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3
Q

What is a main difference between mediation and moderation

A

Mediation shows how a predictor works,

Moderation shows whether or when it works.

shows us under what conditions we can expect a relationship

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4
Q

What is the difference between moderation mediation and a third variable problem

A

Third variable problem:

3rd variable
The mediator is predicting both the main predictor and the outcome.

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5
Q

What is some language showing you have a moderation

A

“Only when” “Sometimes” “It depends”

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6
Q

How does a moderator impact the relationship of the predictor to the outcome

A

Depending on the level of the moderator, the beta will increase or decrease in strength

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7
Q

Which type of variable is easier to visualize in a moderation analysis

A

categorical moderator (as opposed to continuous)

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8
Q

What extra step do you need to do to calculate a moderation analysis, as opposed to a regular 3-variable mutliple regression

A

We need to add an interaction. The model we run includes 3 predictors instead of 2, but the third is just the multiplication of X by M

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9
Q

Which elements are part of the moderation model

A
  1. Predictor
  2. Moderator
  3. Interaction: Predictor x Moderator
  4. Outcome
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10
Q

What is an important first step to run a moderation analysis

A

All predictors need to be centered before conducting your regression.
Centering means subtracting the Mean from each observed value.
Conveniently, standardized variables are automatically centered
The interaction term must be calculated using the centered predictors.

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11
Q

How can you tell if you have a significant moderator, and what should you do next

A

If the interaction term beta is significant, then we have found moderation.
You will get three betas: 2 predictors + Interaction
Follow it up with a simple slopes analysis

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12
Q

What are the simple slopes plot, how should you interpret it

A

This plot allows us to visualize the effect.
It will give the average estimate, the low (-1SD) and the high (+1SD) estimate as well as p-values. If the p-values are significant, you can determine which level of X is different form the average.

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13
Q

What are main features of logistic regression

A
  1. Outcome we’re interested in is categorical.
  2. Doesn’t require straight lines
  3. Can use categorical and continuous predictors
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14
Q

What is a binary logistic regression

A

The outcome has only two possibilities

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15
Q

What is the goal of a logistic regression

A

Instead of focusing on the amount of variability in the outcome that is explained, we’re trying to predict which category participants fall into

With binary logistic regression we make a model to predict which of the outcome variable’s two categories each participant falls into, and then check that model against the observed outcome.

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16
Q

What are the minimum and maximum value of logistic regression

A

Probability ranges between 0 and 1.

You can only have zero if the bottom of the equation reaches infinity, which won’t happen. But in theory, it could reach zero.

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17
Q

What statistics tell us if our logistic regression is significant

A

Our overall model significance test isn’t an ANOVA, but rather a χ2 test (chi squared); this will tell us whether our R2, or accuracy, is high enough

We also want to know how much each predictor contributed to this model accuracy (beta, or other statistics)

18
Q

What should you do if a predictor is not significant in your logistic regression model

A

Remove it.

Just like linear regression, it’s best to use the simplest model you can get away with. That is, without removing any significant predictors.

This means we only keep predictors if they have explanatory benefit

19
Q

What happens if only one of the categories of a predictor has a significant beta?

A

if one of the levels of the categories in that predictor is significant, it justifies using the entire predictor. Not all levels have to be significant

20
Q

What can you use to make sure the predictor you removed was not significant

A

The hierarchical model teardown works well:
First fit a model with all predictors, then remove any that don’t contribute significantly

In jamovi we need to do this backwards, to get the p –value of the model change (to verify we didn’t remove too much)

21
Q

Name the 5 assumptions of logistic regression model

A

Complete Predictors
No Complete Separation
No Overdispersion
Not too much Multicollinearity: continuous predictors only
No Influential Outliers: continuous predictors only

22
Q

Explain complete predictor

A

We need data from all categories, for categorical predictors
We need the full range of responses for continuous predictors

23
Q

Explain complete separation

A

Complete separation is when the outcome is perfectly predicted. Complete separation makes it impossible to select a single wellfitting model (it’s like not being able to calculate a line of best fit) because there is a horizontal gap between the observations

We need to see some horizontal overlap between the high and low probability observations.

24
Q

How can you assess if there is complete separation

A

You can use a Descriptives analysis to determine whether this is a problem.
You need to examine the range (Minimum & Maximum) of scores for each predictor, separately for people in the DV = 0 and DV = 1 categories
Assuming you coded them as 0 and 1, of course

Go to Exploration Descriptives
Add any predictors to the Variables box
Add your outcome variable to the Split by box

25
Q

Explain overdispersion

A

The variance is larger than expected from the binomial distribution.

Essentially, there are too many observations in one condition. It’s only relevant when you have more than one predictor
This would be the same as a violation of the assumption of Independence of Errors in MR – questionable model p -values

It’s still very unlikely to be a problem as with a large sample size, it is very unlikely that our significance would change enough to change the results

underdispersion is also possible, but even more unlikely

26
Q

How can you check for multicollinearity in logistic regression

A

While we could just do a regular linear regression to check for multicollinearity problems, jamovi also has this option under the Assumption Checks
It does the exact same thing, and gives you VIF/Tolerance
Assuming you are using continuous predictors

27
Q

How can you check for outliers in logistic regression

A

For influential outliers we need to do a linear regression, so that we can do Mahalanobis and Cook’s distance checks
We can’t do it 100% correctly (except for Mahalanobis – why?) but it will be approximately right

28
Q

Which statistics could you report from a logistic regression

A

Deviance (aka -2LL) : higher values mean better model fit
Model prediction %
Cox and Snell R2
Nagelkerke R2
McFadden’s R2
Odds Ratio - SPSS called this the Exp(B), just FYI

29
Q

Explain the Odds Ratio

A

The Odds Ratio is the change in the odds of the higher-numbered outcome occurring given a 1 unit change in the predictor.

It is, mercifully, similar to a Beta in that it can show positive and negative relations – but…
If OR is > 1 then the relation is positive
If OR is < 1 then the relation is negative
The OR can’t go below 0, but can go as high as infinity
there is the same amount of space between 0 and 1, then between 1 and infinity using Odds Ratio

1 is our baseline point, as opposed to 0

30
Q

What is the Odds Ratio formula

A

odds after 1 unit change/original odds

Original odds: P(event)/P(no event)

31
Q

How can you interpret a positive Odds Ratio

A

If OR = 3.42, then the probability is 2.42 or 242%

more likely after 1 unit of change in the predictor

32
Q

How can you interpret a negative Odds Ratio

A

If OR = .292, then you must convert it to positive -1/.292 = -3.42. Then the probability is -2.42 or -242%

33
Q

What is the standardized coefficient of a logistic regression and why

A

there are none

Unlike mediation, that’s not something we’ll try to work around
It’s probably best for the situations where you’re likely to use logistic regression
because we are accepting categorical variables, standardizing variables doesn’t necessarily make sense

34
Q

Describe the mixed ANOVA

A

includes at least two different kinds of independent variable and only one dependent variable.

There’s nothing theoretically new about this ANOVA.

You will have at least 2 main effects, and at least 1 interaction

All IVs are categorical
At least one uses the same participants (repeated measures)

At least one uses different participants (independent measures)
Any DVs are continuous

35
Q

What kind of effect are you expected to find in a mixed ANOVA

A

In a Mixed ANOVA design, you get both main effects and interactions among your between- and within-subjects IVs.

Main Effects: An F for each IV
E.g., First Experience of Task (between) & Type of Experience (within)
Interactions: An F for each possible IV combination
E.g., First Experience x Type of Experience (2-way interaction)

36
Q

What should you care the most about when interpreting the result of a mixed ANOVA

A

Interactions tell you there is a complex story to tell, where your outcome (degree of DV) depends on knowing where a person falls on all IVs involved. If present, they’re all you need to care about.

37
Q

Once you find significant F statistics in a mixed ANOVA, what should you do next

A

To properly interpret a mixed ANOVA, you would follow up on your main effects and interactions just as you would for any other ANOVA – with simple effects analyses.

  1. Post-hoc tests are often the best method (recall: Tukey)
  2. Paired-samples t-tests could be required for repeated-measures IVs. To check an interaction, you may need to filter your file to perform these tests on only specific groups
  3. Independent-samples t-tests could be used for between-subjects IVs
  4. Marginal means tables are important for making figures
38
Q

Why do we need to center our variables in the moderation analysis

A

In order to calculate the interaction variable, our data must be centered.
If it is not, we will have too much collinearity violating our assumptions for this model.

Why does it fix the problem? We don’t know, but the statistics demonstrate it

39
Q

When should you worry about overdispersion

A

It’s only relevant when you have more than one predictor

40
Q

How can you test for overdispersion

A

You can’t, but it is highly unlikely to be problematic. Especially with a large enough sample size

41
Q

What type of variables for IV and DV do you need in mixed anova

A

All IVs are categorical

Any DVs are continuous