Week 4 Flashcards
1
Q
Partial Correlation
A
- Useful to detect spuriousness
- Needed to understand
- Factor Anlysis
- Multiple regression
- ANCOVA
- introduces Venn diagriams
2
Q
Factor Analysis
A
- A set of statistical procedures
- Determines the number of distinct unobservable constructs needed to account for the pattern of correlations among a set of measures
3
Q
Correlation in SPSS
A
- r(N-1) = CCA, p<.001
- In this instance coefficient equals .35
- This is greater than .001
- Therefore is significant
4
Q
Bivariate (Zero Order) Correlation (R)
A
- used to determine the existence of relationships between two different variables
- Can be represented with Venn Diagrams
5
Q
Partial Correlation (PR)
A
- Describe the relationship between two variables whilst taking away the effects of another variable, or several other variables, on this relationship.
6
Q
Spurious Correlation
A
- Connection between two variables that appears to be causal but is not.
7
Q
Venn Diagrams
A
Overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.
8
Q
Exploratory Factor Analysis
A
- Data Reduction Technique
- Reveals underlying structure of intercorrelations
- How scale items cluster together
The goal is to summarise the relationships between variables by creating sub-sets of variables
Subsets are known as Factors - Constructs cannot be observed but are inferred by correlations
9
Q
Correlation Matrix
A
a symmetrical square that shows the degree of association between all possible pairs of variables contained in a set.
10
Q
Latent Variables
A
- These are our constructs or factors and cannot be observed
- Can be observed by the way they affect on observable variables
11
Q
Manifest Variables
A
- can be directly observed or measured such as behaviour
- does not need to be inferred
- Used to study latent variables.
- Correlations between them create super-variables or constructs
12
Q
What is Factor Analysis Used For?
A
- Scale Development
- Scale Checking and Refining
- Data Reduction
13
Q
Factor Analysis Uses - Scale Development
A
- Count how many sub-scales we have
- Which items belong to sub-scales
- Which items should be discarded
14
Q
Factor Analysis Uses - Scale Checking and Refining
A
- When used in research does the factor replicate like any previous research?
- Factors are not fixed to any scale: Big Five with University Students vs Nursing Home Residents
- Should I make any changes
- Should be conducted and reported when existing scale is used in research
- Ensure factors are apporpriate for the context
15
Q
Factor Analysis Uses - Data Reduction
A
- To create new Factor Scores
- Can be used as predictors or new outcome variables
- We don’t tend to use this very often
16
Q
Determinant
A
- Individual characteristics, such as cognitions, beliefs and motivation, that could potentially be associated with Constructs
- A determinant > .00001 suggests that multicollinearity is not a problem
17
Q
Multicollinearity
A
- Very high correlation between variables
- If correlations are all small there is no point of running a factor analysis
18
Q
Self Efficacy Scale
A
- 10-item self-report measure of global self-esteem
- Rosenberg rated with 5-point scale strongly agree to strongly disagree
19
Q
Factor Analysis - Preliminary Checks 1 & 2
A
- Look for patterns of correlations between variables
- No point continuing if variables are not correlated
- If correlations are low then we could end up with as many factors as items
20
Q
Zero Order Correlation Matrix
A
- Correlation between two variables without influence of any other variables.
- Same thing as a Pearson correlation.
21
Q
A Determinant
A
- Determinant > .00001 suggests that multicollinearity is not a problem.
22
Q
Factor Analysis
A
- Interpret a factor of a measure
- Uses the correlation of observed variables to estimate latent variables known as factors
- Look for patterns of correlations between variables
- Use factor analysis to identify the hidden variables.
23
Q
Asking in Factor Analysis
A
- Asking if intercorrelations amongst items support separate constructs
- How many constructs do we really need to summarise the items
- Which items belong to each construct
- There is no point in continuing if the variables are not correlated
24
Q
Zero Order Correlation Matrix
A
- Looks at correlations between each pair of variables without considering the influence of any other variables
- Don’t run factor analysis if correlations are small this results in too many factors
- Too much correlation indicates multicollinearity
25
Q
Multicollinearity
A
- When too many items correlate in a Zero Order Correlation Matrix
- If determinant is >.00001 then multicollinearity is not a problem
- We need to have healthy correllations but not to high
26
Q
Preliminary Check 3 & 4
A
- Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy
- Partlett’s test of Sphericity
- Tell you if there are sufficient correlations to make factor analysis worthwhile
27
Q
Kaiser-Meyer-Olkin Measure of Sampling Adequacy - (KMO)
A
- If the variables are all correlated then partial correlation should be small
- proportion of variance in your variables that might be caused by underlying factors
- Venn Diagrams - When we remove all the variance of other variables there is not much left in original correlation
28
Q
Bartletts Test of Sphericity
A
- HO: Does not depart significantly from an identity matrix
- Correlations all close to zero
- Compare our correlation matrix to an identity matrix
- Bartlett’s test is significant at (p<.05)
29
Q
Identity Matrix
A
- A square matrix in which all the elements of principal diagonals are one, and all other elements are zeros
- Shows perfect correlation between each item
- But No correlation - Also Perfectly between each other
- We want to reject this Null Hypothesis
30
Q
Estimated Initial Communalities
A
- Estimated proportion of shared common variants in each item
- Total variance is always 1
- Initial is the proportion of variance that is shared
- What is left over is unique to that item
31
Q
Common Variance
A
- The proportion of overlap between two variables
- Factor analysis is only interested in this variance
- Communalities suggest single Factor
*
32
Q
Specific Variance
A
- What is left over after commonalites with other variables are removed
- Cannot be due to other constructs because they do not correlate
- Isn’t shared with other items
33
Q
Linear Combination of Variables
A
- Expressions constructed from a set of numbers which are multiplied by a constant.
- How much of the data set are common or unique
- How much of the variance can we explain with each factor
- How many factors do we need to extract
- First few factors take up most of the Variance
34
Q
Kaiser Criterion
A
- How many factors should we retain
- Retain factors with eigenvalues > 1
- If they describe more than 1 Item worth of variance then we keep them
- Scree Plot Method draws a line and we are not interested in anything at the bottom
35
Q
Extraction
A
- After extraction only use the variables that remain
- Those that have Common Variance
36
Q
Extracted Communalities
A
- Proportion of Common Variance that can be accounted bor by retained factors
- Extraction Value + Sum of eigenvalues for the extracted factors
37
Q
Previous Preliminary Checks (6)
A
- Bivariate correlations between variables.
- Determinant.
- Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy.
- Bartlett’s Test of Sphericity.
- Extraction
- Initial and Extracted communalities
Are these tapping into underlying constructs?
If they aer too unique then we end up with Items as Factors without correlation
38
Q
A
39
Q
Is Two Factor Solution a Good Solution
A
Several issues to consider:
* Overall proportion of variance accounted for by the retained factors.
* Proportion of common variance in each item accounted for the retained factors.
* Proportion of non-redundant residuals.
* Coherence of factors.
* Overall parsimony.
40
Q
Parsimony
A
- Focuses on using simplicity to understand complex situations and make difficult decisions with confidence
- Helps avoid ambiguity
41
Q
Overall Proportion of Variance
A
- When factors with eigenvalues <1 are removed
- No hard & fast rules but higher is better
- Generally proportion accounted for is > 50% is good
- > 70% is considered very good
42
Q
Proportion of Common Variance
A
- General principle the higher the better
- Seek out low Extracted Communalities
- Anything below 0.3
43
Q
Non Redundant Residuals
A
- More complicated than just asking is our two-factor solution good?
- Use original data to create a two factor model
- If good it can predict the original correlations
- Reproduce the correlation matrix from our model
- If data is good then original and reproduced models should look similar
- Any errors are called residuals
