Multivariate Analyses Flashcards
When is multivariable analysis used?
For data with one dependent variable but more than one independent variable
What is multivariable analysis used to determine
Relative contributions of different causes to a single event or outcome
When is multivariate analysis used?
For data with more than one dependent and independent variable
What is used if both dependent and independent variables are continuous?
Multiple regression
What is used if the dependent variable consists of dichotomous categoric data (two outcomes)?
Logistic regression
What is used if the dependent variable includes a time factor e.g. a survival curve?
Cox proportional hazards model
What is used if the dependent variable consists of nominal categorical data i.e. more than 2 outcomes
Log-linear analysis
What is used if dependent variable is continuous and independent is categorical?
ANOVA
What does ANOVA stand for?
Analysis of variance
What is used if there are both categorical and continuous independent variables?
ANOCA
What does ANCOVA stand for?
Analysis of covariance
What is path analysis?
Extension of multiple regression
What can path analysis do?
Examine situations where there are several final dependent variables with chains of influence
What is cluster analysis?
Multivariate tool used to organise variables into homogenous groups or clusters
What does cluster analysis involve the generation of?
A similarity matrix
What does a cluster analysis produce?
A dendogram
What is canonical correlation?
A multivariate tool used to explore the relationship between two sets of variables
What does canonical correlation involve?
Computation of eigenvalues
What is discriminant function analysis?
Multivariate technique used to detect which of several variables best discriminates between 2 or more groups
What is discriminant function analysis similar to?
Computationally similar to MANOVA
What does MANOVA stand for?
Multivariate analysis of variance
Key uses of multivariate analysis
Look for interaction between independent variables
Quantify associations
Adjust for potential confounders in controlled study
Develop models to predict values or probabilities of certain outcomes
What test to use if dependent variable is nominal categorical?
Log linear analysis
What test to use if dependent variable is categorical dichotomous?
Logistic regression
What test to use if dependent variable is categorical dichotomous with a time factor?
Cox proportional hazards
What test to use if dependent variable is continuous and independent variable is categorical?
ANOVA
What test to use if dependent variable is continuous and independent variable is continuous?
Multiple regression
What test to use if dependent variable is continuous and independent variable is categorical and continuous?
ANCOVA
What does factor analysis refer to?
Set of statistical methods used to detect underlying patterns in relationships among a number of observed variables
Aim of factor analysis
To identify whether correlations between a set of multiple observed variables can be summarised in terms of a smaller number of underlying, latent, unobserved variables called factors
Two approaches of factor analysis
Exploratory
Confirmatory
When is exploratory factor analysis used?
For preliminary investigation of a set of multiple observed variables
What does exploratory factor analysis not do?
It does not make an a priori assumption about the composition of underlying latent variables or factors
Applications of exploratory factor analysis
Data reduction when multiple (>25) variables have been measured, to provide a parsimonious description of the data.
Classification of sx into clinically meaningful concepts
Definition of subscales of new measures
What is confirmatory factor analysis used for?
To test whether a specified factor structure remains valid with new dataset
When is confirmatory factor analysis used?
For assessing construct validity of questionnaires or tests
Stages of factor analysis
Construction of correlation matrix Extraction Rotation measuring the eigenvalues Define factors to be retained Include as many factors as required Labelling
What types of methods are used in extraction?
Common factor analysis
Principal components analysis
What is the eigenvalue
Eigenvalue is the amount of total variance explained by each factor
How can we determine the number of factors to be retained?
Kaiser rule
Scree plot
Include as many factors as required until adequate preset proportion of variation is explained by them
What is kaiser rule?
Only factors with eigenvalues greater than 1 are retained
What is scree plot?
Plot the component numbers against eigenvalues.
Choose the number that forms the bend before the plot levels off on the right side
What happens during labelling and reporting factors?
There is general consensus that variables with a factor loading grater than or equal to 0.4 are probably making a significant contribution to that factor in contrast to those with smaller factor loading
What is path analysis?
Causal modelling and prediction beyond simple regression
What happens in path analysis?
A set of independent variables is related to a set of dependent variables
When is path analysis used?
To examine situations where there are various chains of influence amongst variables studied.
How is a path relationship displayed?
Using arrows that display presumed causal relations.
What is the name of the independent variable in path analysis?
Exogenous variable
What is the name of the dependent variable in path analysis?
Endogenous variable
What does single headed arrow mean in path analysis?
Flows from putative cause to effect
What does double headed arrow suggest in path analysis?
Mere correlation but no predictive, causal link
What is a path coefficent in path analysis?
Indicates the direct effect of a variable assumed to be a cause on another variable assumed to be the effect
What are the two subscripts with which path coefficients are written?
P21 is the path from 1 to 2
i.e. effect is listed first
What is recursive in path analysis?
Path analysis in which the causal flow is unidirectional
When is stratification used?
To control for or analyse the effect of confounder variables
What is a stratum?
Sub-group within a sample often defined by presence or absence of variable of interest
Importance of stratifying data according to confounder variables
Later one can analyse each strata to find the degree of association between presumed cause and effect
What is adjustment in stratification?
When we later produce a single overall estimate using various methods for obtaining summary risk values
Why is a method of weighting suggested for stratification?
Crude summary may not reflect actual risk
How can one use weighting for stratification?
Mantel-Haenszel procedure
What can Mantel-Haenszel procedure be used for in stratification?
Weighting
Help to find if variable is just an efect modifier or real confounder
What is standardised?
Method used in large data sets for public health statistics to produce adjusted rates
What is used for standardisation in public health?
Hypothetical standard population produced by WHO
Types of standardisation
Direct
Indirect
What happens in direct standardisation?
Stratum specific rates from study sample are applied to standard population
What does direct standardisation produce?
Summary score
What happens in indirect standardisation?
Stratum specific rates from standard population are applied to study sample
What does indirect standardisation give?
Expected rates
How does one arrive at standardised rates from expected rate?
Expected rate is divided by the observed rate
What type of confounder is stratification useful for?
Known confounders only
What can adjustment be applied to?
Relative Risk
Odds ratio
What happens to sub-strata risk if the third variable is neither an effect modifier nor a confounder?
Sub-strata risk does not differ from crude total risk
What happens to adjusted vs non-adjusted risk if the third variable is neither an effect modifier nor a confounder
Summary risk does not differ much from crude total risk
What happens to sub-strata risk if the third variable is both an effect modifier and a confounder?
Sub-strata risk differs from crude total risk
What happens to summary risk if the third variable is borth an effect modifier and a confounder?
Summary risk differs from crude total risk
What happens to sub-strata risk if the third variable is an effect modifier but not a confounder?
Sub-strata risk differs from crude total risk
What happens to summary risk if the third variable is an effect modifier but not a confounder?
Summary risk does not differ much from crude total risk
What happens to substrata risk if the third variable is a cofounder but not an effect modifier?
Substrata risk does not differ from crude total risk
What happens to summary risk if the third variable is a confounder but not an effect modifier?
Summary risk differs from crude total risk