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Honours Stats > Week 4 > Flashcards

Week 4 Flashcards

1
Q

What does PCA stand for?

A

Principal Component Analysis (PCA)

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2
Q

What essentially is Principal Component Analysis (PCA)?

A

Combining variables into weighted sums

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3
Q

What essentially is Factor Analysis

A

A technique for showing relationships among variables by relationships to hypothetical underlying factors aka LATENT VARIABLES

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4
Q

Principal Component Analysis (CFA) uses correlation as the underlying association among variables, but Factor Analysis does not, True/False?

A

FALSE

They both use correlations as the underlying thing

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5
Q

How would you characterise the difference between Principal Component Analysis (CFA) and Factor Analysis?

A

PCA looks for ‘optimal linear transformations’ - I don’t know what this means but I’m imagining smushing variables together.

Factor Analysis makes a theoretical assumption that there is an underlying latent variable that explains the observed variables

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6
Q

What determines where you draw the line for the FIRST PRINCIPAL COMPONENT?

A

The line that minimises the diagonal lines to each of the data points (there’s probably a more technical way to say that) - and I think that line is based on something called the EIGEN VECTOR

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7
Q

What even is the SECOND PRINCIPAL COMPONENT?

A

I think it might actually be the original data, but I’m not sure

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8
Q

What is the name given to the VARIANCE of the FIRST PRINCIPAL COMPONENT?

A

The first EIGENVALUE

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9
Q

What do the weights of the first principle component always add up to?

A

1

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10
Q

What is one of the rules for determining the SECOND PRINCIPAL COMPONENT?

A

It must have zero correlation with the FIRST principle component

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11
Q

What’s the limit to number of principal components you can have?

A

It is based on the number of variables you have.

Number of variables = max principal components

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12
Q

Is principle component analysis a MATHEMATICAL or a STATISTICAL technique? And why

A

It’s mathematical

It’s based on matrix algebra

It doesn’t contemplate error values

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13
Q

According to Kaiser’s rule, when should you cut off the number of factors/components?

A

When the Eigenvalue drops below 1

Aka Kaiser-Guttman

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14
Q

Do we like the Kaiser-Guttman rule?

A

NO!

Always tends to chose a third of the variables.

Schmitt says it is “the most inaccurate” of all methods

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15
Q

What are the four methods for determining how many components/dfactors to use

A
  1. Kaiser-Guttman (don’t use)
  2. Scree plot
  3. Parallel Test (the one that uses random data)
  4. MAP test (the Minimum Average Partial Correlation test) Velicer(1976)
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16
Q

What do you use the Parallel Test for?

A

Deciding how many factors/components to use.

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17
Q

When doing the Parallel Test, do you use the mean of the random data or the 95th percentile?

A

I think you use the 95th percentile.

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18
Q

When examining your component loadings - I think it’s in a FACTOR LOADING MATRIX - it is common practice to remove any loadings that are less than 0.5, True/False?

A

FALSE

But close. You can remove any with a loading of less than 0.3.

This is called SUPPRESSING THE LOADINGS

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19
Q

In factor analysis, after extracting your factors/components, you are going to want to do some ROTATION. What are the two types of rotation you can do

A

Orthogonal and Oblique

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20
Q

What assumption underpins ORTHOGONAL rotation?

A

The factors and UNcorrelated

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21
Q

What assumption underpins OBLIQUE rotation?

A

The factors ARE correlated

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22
Q

In psychology, are you more likely to do ORTHOGONAL or OBLIQUE rotation?

A

OBLIQUE

In other words, the one that allows the factors to correlate

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23
Q

When you do oblique rotation, you will get two matrices of loadings. What are they called?

A

The factor PATTERN matrix, and

the factor STRUCTURE matrix

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24
Q

What does the factor PATTERN matrix contain?

A

The regression coefficients… of something

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25
Q

What does the factor STRUCTURE matrix contain?

A

The correlations… of something

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26
Q

Of the two matrices of leadings that we get upon completing a rotation, which one do we generally report?

A

The factor PATTERN matrix

27
Q

If you do an OBLIQUE rotation, the PATTERN and the STRUCTURE matrix are the same thing, T/F?

A

FALSE

They are only the same thing if you do an ORTHOGONAL rotation

28
Q

With FACTOR ANALYSIS, what is our aim in relation to PARTIAL CORRELATIONS between observed variables?

A

We want the PARTIAL CORRELATIONS to be as close to zero as possible

29
Q

In factor analysis, what is the name given to the VARIANCE that is die to the COMMON FACTORS?

A

The COMMUNALITY

30
Q

In factor analysis, what is the opposite of COMMUNALITY?

A

The UNIQUE VARIANCE

… because communality refers to the variance in the observed factors that is due to the common factors.

31
Q

Exploratory Factor Analysis works best with ordinal data, T/F?

A

FALSE

It assumes continuous data (ie Interval or ratio)

You can proceed, but you’ve just gotta note the limitations

32
Q

Missing data is a big deal for Exploratory Factor Analysis, T/F

A

TRUE

Can’t have missing data. Either impute the data or delete the case.

33
Q

Is Exploratory Factor Analysis sensitive to sample size?

A

Big time

34
Q

If you have LOW CORRELATIONS between variables to begin with, is this a good or bad sign for Exploratory Factor Analysis?

A

Bad sign

Factor analysis is based on the assumption that there is some common thing going on, so low correlations means you might be on a hiding to nothing

35
Q

How can you test whether your variables have a high enough correlation to run Exploratory Factor Analysis?

A

Yep, it’s called BARTLET’S TEST, but we don’t like it

36
Q

When doing Exploratory Factor Analysis, does linearity matter?

A

Totes

37
Q

If you have low PARTIAL CORRELATIONS between variables to begin with, is this a good or bad sign for Exploratory Factor Analysis?

A

Good sign

Don’t ask me why

38
Q

When doing Exploratory Factor Analysis, do OUTLIERS matter?

A

Yup

Cos Pearson’s r isn’t robust to outliers

39
Q

If you have CRAZY HIGH correlations (multicollinearity) between variables to begin with, is this a good or bad sign for Exploratory Factor Analysis?

A

Bad sign

You don’t want them two high or two low

40
Q

What is Kaiser’s Measure of Sampling Adequacy about?

A

It’s an overall statistic that tells you how suitable your dataset is for factor analysis

It has something to do with image and anti-image

41
Q

What is the minimum value for Kaiser’s Measure of Sampling Accuracy - that is, the one that signals unacceptability?

A

below .5

42
Q

When you’re looking at an Anti-Image matrix following a Kaiser’s Measure of Sampling Accuracy, what do we want to the values ON the DIAGONAL to approach

A

Approach 1

43
Q

When you’re looking at an Anti-Image matrix following a Kaiser’s Measure of Sampling Accuracy, what do we want to the values OFF the DIAGONAL to approach

A

Approach zero

44
Q

What are the TWO major methods of finding factors in SPSS (the ones that Schmitt (2011) recommends.

A
  1. Maximum likelihood (ML)

2. Principle axis factoring (PA)

45
Q

Under what circumstances would you use PRINCIPAL AXIS FACTORING (PA) when finding factors?

A

If your data is not normally distributed

46
Q

Under what circumstances would you use MAXIMUM LIKELIHOOD (ML) when finding factors?

A

I think when you want to generalise to the general population

Note: requires normal distribution

47
Q

What does it mean when you see .999 in a factor loading table?

A

It’s a Heywood case

It means there is an error

48
Q

What is the term given to when you weight each factor loading the same (hint: equivalently)?

A

Tau-equivalent

49
Q

What are the three ways SPSS provides for estimating factor scores? And which is the one Geoff recommends, and why?

A
  1. a regression method
  2. the BARTLETT method (actually Maximum Likelihood or Weighted Least Scores)
  3. ANDERSON-RUBIN

Geoff recommends BARTLETT, because for oblique solutions Anderson-Runin is misleading because it assumes uncorrelated scores.

50
Q

What are the SIX differences that Geoff highlights between PCA and FA?

A
  1. Principle Components = linear combinations of obersved variables. Factors = theoretical entities.
  2. In FA, error is explicitly modelled. Not so for PCA.
  3. In FA, if factors are removed/added, the other factor loadings change. Not so for PCA
  4. FA is a theoretical modelling method (so can test model fit). Not so for PCA.
  5. FA ‘fragments’ variability into common and unique parts. Not so PCA
  6. PCA has a canonical algorithm that always works. FA has many, which need to be matched to the data
51
Q

Do FA and PCA have the same general form?

A

Yes, and it goes like this:

Observed Variable = Loading x F + error

Where F is either a factor or a component

52
Q

Do FA and PCA typically deliver similar results?

A

Yes, particularly if they’re applied to a large number of variables and a large sample size

53
Q

What is the tip provided by a past tutor in the subject about when to use PCA and when to use FA

A

Use FA is you assume or wish to test, a theoretical model of latent factors causing observed variables

Use PCA if you simply want to reduce your correlated observed variables into a smaller set of important uncorrelated composite variables

54
Q

With Varimax rotation, why would you not get both pattern and structure matrices?

A

Because Varimax is a form of ORTHOGONAL rotation, and because orthogonal rotation produces perfectly uncorrelated stage, you end up with pattern and structure matrices that are identical. Hence no need to produce both.

55
Q

The Promax rotation technique is an OBLIQUE technique, which means factors are allowed to be correlated, thus it produces pattern AND structure matrices. But why?

A

The pattern matrix shows factor loadings

The structure matrix shows correlation between the variable and the factor.

The factor loadings in the pattern matrix PARTIAL OUT any common variation among factors

56
Q

If you square and sum each of the factor loadings for a single VARIABLE, what do you get?

A

The COMMUNALITY for that variable

57
Q

If you square and sum each of the factor loadings for a single FACTOR, what do you get?

A

The EIGENVALUE for that Factor

58
Q

If your data is not normally distributed, should you be cautious about using EFA?

A

Nope, you just need to make sure you use the PRINCIPAL AXIS FACTORING extraction method

59
Q

If you have as many items measured as you have participants, should you be cautious about using EFA

A

YES FFS

Some people say you need st least 20 items per participant

60
Q

If your MSA is below 0.5 should you worry about using an EFA? Why tho

A

Yes

Because a low MSA score means the correlation between your variables is quite low.

This means there is little common variance for you to extract, so you probably won’t get any factors that explain multiple items well

61
Q

If some of your commonalities are equal to or greater than 1.0, should you be worried about doing an EFA?

A

Totes

A communality score of 1 means there’s basically no unique variance

If this happens, computer will set a very high communality factor as a kind of error signal. This is the origin of Heywood cases.

62
Q

What is an Eigenvalue anyway? No, really, what actually is it

A

It is the variance explained by a principal component

If it is about components, why are we thinking about it in relation to EFA? Nobody knows

63
Q

Imagine you’re doing a EFA.

Using SPSS outputs, how do you tell which item is explained WORST by the extracted factors?

A

First, you look at the COMMONALITIES table

Then you find the one with the LOWEST score

REASON: Communalities reflect the sum of squared factor loadings and thus, a low communality means low factor loadings

64
Q

In EFA, one of the benefits of rotating the factors is to increase the total variance explained, T/F?

A

FALSE

Rotation will never affect the total explained variance, it will only affect how each factor contributes towards this total.

Honours Stats (3 decks)

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