WK 10 Flashcards

1
Q

What is the key feature that distinguishes factor analysis and principal component analysis?

A

Latent variables

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2
Q

What do latent variables do?

A

Explains correlations between measured variables

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3
Q

In PCA what are the observed measures?

A

The observed measures are independent variables

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4
Q

In PCA what is the component (z)?

A

The component is the dependent variable

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5
Q

What does PCA explain?

A

It explains as much variance in the measures as possible
- goal of PCA is to explain/ account for all possible variance by this reduced set

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6
Q

In PCA what are the components?

A

The components are determinate

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7
Q

In EFA, what are the observed measures?

A

They are the dependent variables?

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8
Q

In EFA, what is the factor?

A

It is the independent variable

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9
Q

What does EFA model?

A

EFA models the relationship between variables
- In factor analysis, we are not concerned by all variance but rather common variance

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10
Q

In EFA, what are indeterminate?

A

Factors

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11
Q

What are correlations?

A

standardized covariates

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12
Q

What does EFA try to explain?

A

Tries to explain patterns of correlations

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13
Q

What does factor analysis have to distinguish?

A

Factor analysis has to distinguish between the true and unique variance

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14
Q

What is true variance?

A

True variance is variance common to an item and at least one other item as well as variance specific to an item that is not shared with any other items

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15
Q

What is unique variance?

A

Variance specific to an item that is not shared with any other items and error variance

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16
Q

What is the issue with unique variance?

A

We cannot distinguish between unique variance and error variance in the model -> all we know is that it is not shared

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17
Q

What is the error term?

A

when we see the error term in factor analysis it comprises of var(specific) + var(error) -> It is both legitimate error and the bit of variance in the item that is not shared

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18
Q

What are the assumptions in EFA?

A
  • the residual/ error terms should be uncorrelated
  • the residual/errors should not correlate with factor
  • relationships between items and factors should be linear
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19
Q

What is the estimation method in EFA?

A

We need to estimate the model parameters -> primarily here the factor loading’s

20
Q

When we run a FA, what is the main element of our output?

A

Factor loading’s and factor correlations

21
Q

What do factor loadings show?

A

They show the relationship between the measured variable and factor

22
Q

How do we interpret out factor models?

A

Interpret our factor models by the pattern and size of these loading’s

23
Q

What are primary loadings?

A

They refer to the factor on which a measured variable has it’s highest loading

24
Q

What are cross-loadings?

A

They refer to all other factor loadings for a given measured variable

25
Q

What is the range of factor loadings?

A

they range between 1 and -1

26
Q

If we have a good factor solution, what will the sizes of the loadings be?

A

primary loadings should be big and all other loadings are small

27
Q

What is the most efficient way to factor analyze data?

A

To start by estimating communalities

28
Q

What are communalities?

A

Communalities are estimates of how much true variance any variable has

29
Q

Why is estimating communalities hard?

A

It is hard because population communalities are unknown

30
Q

What is the range of communalities?

A

They range from 0 (no shared variance) to 1 (all variance is shared)

31
Q

What is a heywood case?

A

A communality estimate larger or equal to 1

32
Q

What are the issues with MLE?

A

non-convergence issues

33
Q

What is the assumption with constructs we seek to measure by questionnaire?

A

They are assumed to be continuously distributed

34
Q

In factor analysis, how do we decide on the number of factors?

A
  • visualise eigenvalues with scree plot
    -treat MAP as a minimum and power analysis as maximum
  • explore all solutions in this range and select the one that yields the best numerically and theoretically
35
Q

What is factor rotation?

A

It is an approach to clarifying the relationships between items and factors

36
Q

What is the aim of rotation?

A

Rotation aims to maximise the relationship of a measured item with a factor
(Make the primary loafing big and cross loadings small)

37
Q

What does orthogonal rotation include?

A

Includes varimax and quartimax rotations

38
Q

What are the criteria of orthogonal rotations?

A

Orthogonal rotation factors are not allowed to correlate with each other (correlations are zero) , and their axes are at right angles

39
Q

What does oblique rotations include?

A

Includes promax and oblimin rotations

40
Q

What are the criteria of oblique rotations?

A

They are allowed to have correlations between factors (correlations are not zero), and their axes are not at right angles

41
Q

How do I choose which rotation?

A

Always choose oblique

42
Q

Why should you always choose oblique rotation?

A

It is very unlikely factors have correlations of 0, if they are close to 0, they are allowed within oblique rotation

43
Q

When we have an obliquely rotated solution, what do we need to draw a distinction between?

A

We need to draw a distinction between the pattern and structure matrix

44
Q

What is a pattern matrix?

A

Pattern matrix : matrix of regression weights (loadings’) from factors to variables

45
Q

What is a structure matrix?

A

the structure matrix is the pattern matrix multiplied by the factor correlations