Podcast
Questions and Answers
What is a key indicator that a retained factor is meaningful in PCA?
What is a key indicator that a retained factor is meaningful in PCA?
- Eigenvalues = 0
- Eigenvalues > 1 (correct)
- Eigenvalues = 1
- Eigenvalues < 1
In exploratory factor analysis (EFA), a factor should ideally have at least 1 item for reliability.
In exploratory factor analysis (EFA), a factor should ideally have at least 1 item for reliability.
False (B)
How much variance should retained factors ideally explain in PCA?
How much variance should retained factors ideally explain in PCA?
70%
Factors should be conceptually meaningful, and loadings should align well with __________ expectations.
Factors should be conceptually meaningful, and loadings should align well with __________ expectations.
Match the following indicators with their descriptions:
Match the following indicators with their descriptions:
What is one of the main goals of Principal Component Analysis (PCA)?
What is one of the main goals of Principal Component Analysis (PCA)?
Eigenvalues in PCA represent how much variance each principal component captures.
Eigenvalues in PCA represent how much variance each principal component captures.
PCA can help in reducing dimensionality by transforming __ constructs into three.
PCA can help in reducing dimensionality by transforming __ constructs into three.
Match the following PCA components with their descriptions:
Match the following PCA components with their descriptions:
Which criterion is commonly used to decide the number of components to retain in PCA?
Which criterion is commonly used to decide the number of components to retain in PCA?
In PCA, components need to be correlated with each other to effectively explain variance.
In PCA, components need to be correlated with each other to effectively explain variance.
What procedure is applied in PCA to calculate a set of linear composites?
What procedure is applied in PCA to calculate a set of linear composites?
What is the primary purpose of eigenvalues in the context of a data set?
What is the primary purpose of eigenvalues in the context of a data set?
Eigenvalues allow for the reduction of dimensions without any loss of information.
Eigenvalues allow for the reduction of dimensions without any loss of information.
What is the Kaison criteria related to eigenvalues?
What is the Kaison criteria related to eigenvalues?
The sum of the eigenvalues will equal the number of _____ in the data set.
The sum of the eigenvalues will equal the number of _____ in the data set.
Match the methods for deciding how many components to retain with their descriptions:
Match the methods for deciding how many components to retain with their descriptions:
Which of the following statements is true regarding eigenvectors?
Which of the following statements is true regarding eigenvectors?
A component with an eigenvalue less than 1 is considered significant in the context of PCA.
A component with an eigenvalue less than 1 is considered significant in the context of PCA.
How much of the total variance is captured by all the eigenvalues together?
How much of the total variance is captured by all the eigenvalues together?
Flashcards
Factor Analysis
Factor Analysis
Factor analysis aims to find a smaller set of underlying factors that explain the relationships between observed variables.
Scree Plot
Scree Plot
A visual representation of eigenvalues, showing the amount of variance explained by each factor, used to determine the optimal number of factors.
Parallel Analysis
Parallel Analysis
A method for evaluating the number of factors by comparing eigenvalues to those from random data, helping to avoid overfitting.
Sufficient Items Per Factor
Sufficient Items Per Factor
When a factor has at least 3-4 variables strongly associated with it, indicating its stability and clarity.
Signup and view all the flashcards
Total Variance Explained
Total Variance Explained
Indicates how well the retained factors explain the overall variance in the data, a high percentage (>70%) is desirable in PCA.
Signup and view all the flashcards
Principal Component Analysis (PCA)
Principal Component Analysis (PCA)
A statistical technique that reduces the dimensionality of a dataset by identifying underlying patterns and creating new, uncorrelated variables called principal components.
Signup and view all the flashcards
Multicollinearity
Multicollinearity
A situation where two or more independent variables in a regression model are highly correlated with each other, making it difficult to determine their individual effects on the dependent variable.
Signup and view all the flashcards
Explained Variance
Explained Variance
The amount of variation explained by each principal component, measured as a percentage of the total variance in the dataset.
Signup and view all the flashcards
Loadings
Loadings
Values that represent the correlation between each original variable and the corresponding principal component.
Signup and view all the flashcards
Scores
Scores
The representation of original data points in the new space defined by principal components.
Signup and view all the flashcards
Component Selection
Component Selection
The process of selecting the number of principal components to retain based on criteria like the Kaiser criterion or scree plot analysis.
Signup and view all the flashcards
Kaiser Criterion
Kaiser Criterion
A criterion for component selection where principal components with eigenvalues greater than 1 are retained.
Signup and view all the flashcards
Scree Plot Analysis
Scree Plot Analysis
A visual representation of eigenvalues, typically plotted as a descending line, which helps to determine the 'elbow' point where the rate of decrease in eigenvalues starts to flatten out, indicating the optimal number of components to retain.
Signup and view all the flashcards
Total Variance and Eigenvalues
Total Variance and Eigenvalues
The sum of all the eigenvalues of a matrix represents the total amount of variance in the original data set.
Signup and view all the flashcards
What are Eigenvalues?
What are Eigenvalues?
Eigenvalues are numerical values representing the variance captured by each component in a PCA analysis. They indicate how much variance each component explains.
Signup and view all the flashcards
What are Eigenvectors?
What are Eigenvectors?
Eigenvectors are vectors that define the direction and magnitude of each principal component in a PCA analysis. They indicate how much each item 'contributes' to a given component.
Signup and view all the flashcards
Kaison Criteria
Kaison Criteria
The 'Kaison Criteria' (eigenvalue > 1) is a simple rule of thumb for selecting principal components in PCA. It suggests keeping components with eigenvalues greater than 1, as they explain more variance than a single variable.
Signup and view all the flashcards
Goal of Principal Component Analysis (PCA)
Goal of Principal Component Analysis (PCA)
PCA aims to preserve the most important information by grouping variables into meaningful components. It aims to capture as much variance as possible while reducing data dimensionality.
Signup and view all the flashcards
PCA and Dimensionality Reduction
PCA and Dimensionality Reduction
PCA repackages the variance of the original data into a new set of components, but it does not reduce the number of dimensions directly.
Signup and view all the flashcards
Scree Plot Method
Scree Plot Method
The 'Scree Plot' method involves plotting the eigenvalues in descending order. You look for an 'elbow' in the plot where the rate of change of eigenvalues decreases significantly. This point suggests the number of components to retain.
Signup and view all the flashcardsStudy Notes
Psychometric Testing
- Focuses on measuring psychological constructs through questionnaires and scales.
- Involves understanding constructs, ensuring reliability and validity of measurements, and managing questionnaire data effectively.
Psychological Constructs
- Abstract concepts like intelligence, stress, or satisfaction.
- Measured indirectly through questions or items.
- Operationalized to become measurable variables (e.g., a questionnaire on stress levels).
- Different operationalisations make consolidating findings difficult.
Jingle and Jangle Fallacies
- Jingle fallacy: Using the same name to denote different things.
- Example: Two narcissism scales, both using similar names but measuring different aspects.
- Jangle fallacy: Using different names to denote the same thing.
- Example: Creating new measures of a construct without considering existing measures.
- This can lead to inconsistent research findings and create unnecessary redundancy.
Connections
- Connects observable phenomena (e.g., item responses) to theoretical attributes (e.g., life satisfaction).
- Psychometricians study the conceptual and statistical foundations of constructs.
- Psychometrics applies across many sciences (e.g., psychology, behavioural genetics, neuroscience, political science, medicine).
- Tests of typical performance measure what participants do regularly (e.g., interests, values, personality, beliefs, as in the "Harry Potter House" quiz.)
- Tests of maximal performance measure performance when participants exert maximum effort (e.g., aptitude tests, exams, cognitive tests).
Types of Psychometric Tests
- Education: Aptitude and ability tests (standard school tests), vocational tests.
- Business: Selection (e.g., personality, skills), development (e.g., interests, leadership), performance (e.g. well-being, engagement).
- Health: Mental health symptoms (e.g., anxiety), clinical diagnoses (e.g., personality disorders).
Criteria for Psychometric Tests
- Validity: The degree to which a test measures what it intends to measure.
- Reliability: The consistency of a measurement over time and various contexts.
- Interpretability: The clarity with which the scores can be understood and used.
- Relevance: The applicability of the test to specific populations or contexts.
Measurement Error
- Random error: Unpredictable and inconsistent values due to factors specific to the measurement.
- Systematic error: Predictable alterations of the observed score due to factors within the measurement.
- Social desirability bias: Tendency to report answers that are socially desirable rather than accurate self-report.
Correlations and Covariance
- Unit of analysis in psychometrics is covariance (relationship between two variables)
- Variance measures how much a variable deviates from the mean.
- Covariance captures how two variables change together.
- Correlation is a standardize version of covariance.
Correlation Coefficient
- Measures the strength and direction of the relationship between two variables.
- Ranges from -1 to 1.
- Indicates a perfect positive correlation = +1 and as one variable increases, the other increases linearly.
Diagrammatical Conventions
- Square: Observed or measured item.
- Circle: Latent or unobserved variable (the concept or construct being measured).
- Two-headed arrow: Covariance (relationship between variables).
- Single-headed arrow: Regression path (indicating the direction of the causal relationship).
Validity
- Content Validity: The extent to which a test adequately measures all important aspects of the construct it's intended to measure.
- Construct Validity: The extent to which a test measures the intended theoretical construct.
- Face Validity: How suitable and relevant the test appears to be for its intended use, in the eyes of the person tasked with taking the test, e.g. using a balloon-blowing task to assess impulsivity.
- Criterion-related Validity: The extent to which a test's results correlate with other measures of the construct (criterion).
Reliability
- Test-retest reliability: Consistency of a test over time.
- Alternate-forms reliability: Consistency between similar tests (or differing versions of a test.)
- Split-half reliability: Consistency between the halves of a single test.
- Internal consistency reliability: How well items within a test measure the same construct (e.g., Cronbach's alpha).
- Inter-rater reliability: Consistency in scoring across different raters or judges when rating the same test subjects.
Scoring in CTT
- Summarising responses to evaluate a psychological construct.
Alternate Forms & Split-Half Reliability
- Correlation between different versions or divided halves of the same test.
Internal Consistency
- How well items on a scale correlate with each other.
Cronbach's Alpha
- Calculates internal consistency reliability of a scale.
Principal Component Analysis (PCA)
- Statistical technique to reduce data dimensionality.
- Transforms many observed variables into fewer uncorrelated principal components.
Factor Analyses (FA)
- Determines underlying latent variables (factors) that contribute to correlations among observed variables.
When to Use PCA or FA
- For dimensionality reduction.
- To understand the structure and relationships between variables.
Structural Validity
- Focuses on understanding the idiosyncratic and expensive process of discovering the factors behind a construct, and then to test whether these factors make sense.
Questionnaire Data Handling
- Data cleaning: Dealing with missing data, coding inconsistencies, and format issues.
- Recoding: Transforming answers to standardise data.
- Reliability: Assessing the consistency of measurement within tests or questionnaires.
- Validity: Ensuring that the instrument measures what it is intended to measure.
- Reverse coding: Adjusting items that are measured inversely.
Psychometric Testing - Steps
- Data importation: Reading data into software.
- Variable renaming: Giving concise names to each variable.
- Recoding responses: Converting data into a usable format (numerical, e.g., Likert scales).
- Reverse coding: Changing the polarity of items when necessary.
- Calculating scale scores: Summing or averaging scores to derive total scores.
- Analysis: Comparing scores to evaluate intervention effectiveness.
Important Considerations
- Item-to-factor relationship: How strongly individual items relate to the factors.
- Factor interpretation: Do the factors derived make sense given the research question?
- Communality: What portion of each variable's variance is explained by the factors.
- Uniqueness: What proportion of variance is not explained.
Evaluating Psychometric Testing
- Validity and reliability: Determining the accuracy and consistency of the test.
- Evaluating factor solutions: Assessing the quality of the factors found, considering item loadings, variance explained, and other concerns.
- Item and factor labels: Determining if labels make sense in the context of the data and research.
Signs of good test design
- Clear, comprehensive measures.
- Clear items and tasks.
- Balanced factors and items.
- Relevant labels for items and factors.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
