Multivariate analyses

Question 1

Multivariable analysis

Answer 1

• used for data with one dependent outcome variable but more than one independent variable
• multivariable analysis determines the relative contributions of different causes to a single event or outcome

Question 2

Multivariate analysis

Answer 2

-used for data with more than one dependent outcome variable as well as more than one independent variable

Question 3

Multiple regression

Answer 3

-used if both the dependent and independent variables consist of continuous data

Question 4

Logistic regression

Answer 4

-used if the dependent variable consists of dichotomous categorical data (two outcomes)

Question 5

Cox proportional hazards model

Answer 5

-used if the dependent variable also includes a time factor (e.g survival curve)

Question 6

Log-linear analysis

Answer 6

-if the dependent variable consists of nominal categorical data (ie more than two outcomes)

Question 7

Analysis of variance (ANOVA)

Answer 7

-for analysis of continuous dependent variable with categorical independent variables use ANOVA

Question 8

Analysis of covariance (ANCOVA)

Answer 8

-used if there are both categorical and continuous independent variables

Question 9

Path analysis

Answer 9

• an extension of multiple regression
• examines situations in which there are several final dependent variables with ‘chains’ of influence ie. variable A influences variable B which in turn affects variable C

Question 10

Cluster analysis

Answer 10

• a multivariate tool used to organise variables into relatively homogeneous groups or ‘clusters’
• involves the generation of a similarity matrix
• produces a dendrogram

Question 11

Canonical correlation

Answer 11

• multivariate tool used to explore the relationship between two sets of variables
• involves the computation of eigenvalues

Question 12

Discriminant function analysis

Answer 12

• a multivariate technique used to detect which of several variables best discriminates between two or more groups
• similar to the multivariate analysis of variance MANOVA

Question 13

Factor analysis

Answer 13

• refers to a set of statistical methods used to detect underlying patterns in the relationships among a number of observed variables
• aims to identify whether the correlations between a set of multiple observed variables can be summarised in terms of a smaller number of underlying, latent, unobserved variables called ‘factors’

Question 14

Two main types of factor analysis

Answer 14

1. exploratory factor analysis

2. confirmatory factor analysis

Question 15

Exploratory factor analysis

Answer 15

• used for the preliminary investigation of a set of multiple observed variables
• doesn’t make assumptions about the compositions of underlying latent variables or factors

Question 16

Applications of exploratory factor analysis

Answer 16

1. data reduction when multiple (over 25) variables have been measured
2. classification of symptoms into meaningful concepts
3. definition of subscales of new measures

Question 17

Confirmatory factor analysis

Answer 17

• method for testing whether a specified factor structure remains valid with a new dataset
• primarily used for assessing the construct validity of questionnaires or tests.

Question 18

Conducting a factor analysis

Answer 18

1. construct a correlation matrix
2 extraction
3. rotation
4. define the factors to be retained
5. labelling

Question 19

Extraction in factor analysis

Answer 19

-common factor analysis and principal components analysis are most frequently used

Question 20

Rotation

Answer 20

-involves measuring the eigenvalues

Question 21

Eigenvalue

Answer 21

-the amount of total variance explained by each factor

Question 22

Kaiser rule

Answer 22

-only factors with eigenvalues greater than 1 are retained

Question 23

Scree plot

Answer 23

• plot the component numbers against eigenvalues

- choose the number that forms the elbow or bend before the plot levels off on the right side

Question 24

Labelling

Answer 24

-there is a general cosensus that the variables with a factor loading greater than or equal to 0.40 are probably making a significant contribution to that factor in constrast to those with smaller factor loadings

Question 25

Defining the factors to be retained

Answer 25

• factor analysis

- eigenvalues are used to work out which values to keep

Question 26

Path analysis

Answer 26

• refers to causal modelling and prediction beyond simple regression
• independent variables are exogenous variables and dependent variables are endogenous
• arrows display presumed causal relations

Question 27

Arrows in path analysis

Answer 27

• single headed arrow flows from a putative cause to the effect
• double headed curve arrow indicates mere correlation but no predictive causal links

Question 28

Path coefficient

Answer 28

• used in path analysis

- indicates the direct effect of a variable assumed to be a cause on another variable assumed to be an effect

Question 29

Stratification

Answer 29

-often used to control or analyse the effect of confounder variables

Question 30

Stratum

Answer 30

-a sub-group within a sample often defined by the presence or absence of a variable of interest

Question 31

Mantel-Haenszel procedure

Answer 31

-applies a method of weighting for each strum to produce a summary score to help create an adjusted RR

Question 32

Standardisation

Answer 32

• another method of stratification used in large data sets for public health statistics to produce adjusted rates
• age is the most often standardised variable
• a hypothetical ‘world standard population’ is often used

Question 33

Direct standardisation

Answer 33

• stratum specific rates from study sample are applied to the standard population
• summary score is produced from this data

Question 34

Indirect standardisation

Answer 34

• stratum specific rates from the standard population are applied to the study sample
• this gives expected rates
• the expected rates are divided by the observed rates to arrive at standadrised rates e.g standardised mortality ratio

Question 35

Key learning points

Answer 35

• stratification is useful only for known confounders
• adjustment can be applied to Odds ratio as well as RR
• multivariate techniques such as regression can also be used for analysing confounders