Factor Analysis: Uncover Hidden Patterns in Data

Question 1

What is the primary goal of factor analysis?

Accepted Answer

To identify underlying latent variables that explain the relationships among observed variables

Answer

To test a hypothesized model.

Answer

To predict future values of a dependent variable based on the values of independent variables.

Question 2

What is the difference between exploratory factor analysis (EFA) and confirmatory factor analysis (CFA)?

Accepted Answer

EFA is a technique used to explore the underlying structure of a dataset, while CFA is a technique used to test a specific, predefined model

Answer

CFA is used to explore the underlying structure of a dataset while EFA is used to test a specific, predefined model.

Answer

EFA is used to analyze large datasets while CFA is used to analyze small datasets.

Question 3

What is the eigenvalue of a factor?

Accepted Answer

The variance explained by a factor

Answer

The number of variables that load on a factor

Answer

The correlation between a factor and a variable

Answer

The percentage of total variance explained by a factor

Question 4

What is the scree plot?

Accepted Answer

A graph used to determine the number of factors to extract from a dataset based on the eigenvalues of the factors

Answer

A graph used to determine the correlation between the variables in a dataset

Question 5

What is the purpose of factor rotation?

Accepted Answer

To make the factors easier to interpret

Answer

To increase the variance explained by the factors.

Answer

To ensure that the factors are uncorrelated.

Answer

To decrease the number of factors.

Question 6

Which of the following is not a recognized type of factor analysis?

Accepted Answer

Iterative factor analysis

Answer

Exploratory factor analysis

Answer

Confirmatory factor analysis

Question 7

Which statement best describes the primary goal of Factor Analysis?

Accepted Answer

To identify underlying latent factors that explain the covariation in a set of observed variables.

Answer

To reduce the number of variables in a dataset without losing substantial information.

Answer

To categorize data points into distinct clusters based on their similarities.

Question 8

In Factor Analysis, the number of factors extracted is typically determined by examining:

Accepted Answer

Eigenvalues and scree plots.

Answer

The sample size.

Answer

A predetermined significance level.

Answer

The number of variables in the dataset.

Question 9

A common application of Factor Analysis in machine learning is:

Accepted Answer

Feature selection and dimensionality reduction.

Answer

Analyzing time series data for patterns and trends.

Answer

Predicting continuous outcomes using regression models.

Answer

Clustering data points into distinct groups.

Question 10

The scree plot is used in Factor Analysis to:

Accepted Answer

Visualize eigenvalues and determine the optimal number of factors to extract.

Answer

Assess the reliability of the extracted factors.

Answer

Identify outliers in the data.

Question 11

Which factor rotation methods can be used in Factor Analysis?

Accepted Answer

Varimax and Promax.

Answer

Hierarchical clustering.

Answer

Principal Component Analysis (PCA).

Answer

K-Means clustering.

Question 12

The Kaiser-Meyer-Olkin (KMO) measure is used to:

Accepted Answer

Assess the suitability of a dataset for Factor Analysis.

Answer

Determine the statistical significance of factor loadings.

Answer

Specify the number of factors to be extracted.

Answer

Evaluate the reliability of the extracted factors.

Question 13

What is the primary goal of factor analysis?

Accepted Answer

To identify underlying, unobserved variables (factors) that explain the relationships between observed variables.

Answer

To group items into categories based on their similarities.

Answer

To predict the value of a dependent variable based on independent variables.

Answer

To reduce the dimensionality of data by identifying a smaller number of representative variables.

Question 14

Which of the following is a key assumption of factor analysis?

Accepted Answer

The variables are linearly related to the underlying factors.

Answer

The factors are independent.

Answer

The number of factors is known in advance.

Answer

The data is normally distributed.

Question 15

What is the main difference between exploratory factor analysis (EFA) and confirmatory factor analysis (CFA)?

Accepted Answer

EFA is used to explore the underlying structure of data without pre-defined hypotheses, while CFA tests specific hypotheses about the factor structure.

Answer

EFA is used with large datasets, while CFA is used with small datasets.

Answer

EFA is a more advanced technique than CFA.

Question 16

What is the purpose of a scree plot in factor analysis?

Accepted Answer

To visually determine the optimal number of factors to extract by identifying an 'elbow' point where the slope of the plot changes.

Answer

To determine the reliability of the factors.

Answer

To identify the factors that are most important.

Answer

To visualize the distribution of the data.

Question 17

What does a factor loading represent in factor analysis?

Accepted Answer

The correlation between a variable and a specific factor, indicating the strength and direction of their relationship.

Answer

The reliability of a factor.

Answer

The variance of a factor explained by a variable.

Answer

The weight of a variable in a factor.

Question 18

Which of the following methods is commonly used to extract factors in factor analysis?

Accepted Answer

Principal Components Analysis (PCA)

Answer

Cluster analysis.

Answer

Regression analysis.

Answer

Discriminant analysis.

Question 19

Which of the following is a potential limitation of factor analysis?

Accepted Answer

Interpreting the meaning and significance of extracted factors can be challenging and subjective.

Answer

It is not suitable for data with missing values.

Answer

It can be computationally intensive.

Answer

It is only suitable for large datasets.

Question 20

How can you assess the reliability of a factor in factor analysis?

Accepted Answer

By examining the factor loadings and the eigenvalues, as well as by assessing the communalities and factor correlations.

Answer

By conducting a reliability analysis.

Answer

By examining the scree plot.

Question 21

What is the key difference between an oblique rotation and an orthogonal rotation in factor analysis?

Accepted Answer

An oblique rotation allows for correlations between factors, while an orthogonal rotation assumes the factors are uncorrelated.

Answer

In an oblique rotation, the factors are extracted from the data, while in an orthogonal rotation, the factors are specified in advance.

Answer

An oblique rotation is more complex than an orthogonal rotation.

Question 22

Which of the following is NOT a benefit of using Factor Analysis?

Accepted Answer

Overfitting the model

Answer

Improving the interpretability of results by simplifying complex datasets

Answer

Identifying underlying factors that explain data variability

Answer

Reducing the number of variables while retaining most of the information

Question 23

What is the primary goal of Factor Analysis?

Accepted Answer

To explain the variance in data by identifying underlying factors

Answer

To predict future outcomes based on historical data

Answer

To create new variables by combining existing ones

Answer

To group similar data points together into clusters

Question 24

Which method is commonly used to extract factors from data in Factor Analysis?

Accepted Answer

Principal Component Analysis (PCA)

Answer

Logistic Regression

Answer

Linear Discriminant Analysis (LDA)

Answer

K-Means Clustering

Question 25

What criterion is generally used to determine the number of factors to extract in Factor Analysis?

Accepted Answer

Eigenvalues greater than 1

Answer

Number of variables in the dataset

Answer

Sample size of the data

Answer

Subjectivity of the researcher based on theoretical knowledge

Question 26

In Factor Analysis, what are the unobservable variables that are inferred from the observed variables called?

Accepted Answer

Latent factors

Answer

Communalities (proportion of variance explained by a factor)

Answer

Manifest variables (the observed variables in the dataset)

Answer

Eigenvalues (variance explained by each factor)

Question 27

What is the primary purpose of using a scree plot in Factor Analysis?

Accepted Answer

To visually determine the optimal number of factors to extract, based on the point of inflection in the plot

Answer

To identify outliers in the data that might be distorting results

Answer

To evaluate the overall fit of the Factor Analysis model

Answer

To check for normality of the data distribution

Question 28

What is the term for the measure of how strongly a variable loads onto a factor in Factor Analysis?

Accepted Answer

Factor loading

Answer

Eigenvalue (variance explained by each factor)

Answer

Discriminant function (used in LDA, not Factor Analysis)

Answer

Communality (proportion of variance explained by a factor)

Question 29

How can Factor Analysis be used to improve the performance of machine learning models?

Accepted Answer

By reducing the dimensionality of the data, potentially improving model efficiency and preventing overfitting

Answer

By making the model more complex, which doesn't necessarily lead to better performance

Answer

By making the model more interpretable, but not necessarily improving its predictive power

Answer

By increasing the number of variables in the model, which can lead to overfitting

Question 30

What is the main difference between exploratory factor analysis (EFA) and confirmatory factor analysis (CFA)?

Accepted Answer

EFA is used to explore the underlying structure of data without pre-defined hypotheses, while CFA tests a specific hypothesis about the structure of data

Answer

EFA is typically used with large datasets, while CFA is used with small datasets, but this is not a defining characteristic

Question 31

What is the primary purpose of factor scores in Factor Analysis?

Accepted Answer

To represent the original variables in terms of the extracted factors, providing a more concise and interpretable representation of the data

Answer

To improve the interpretability of data by providing a simplified view

Answer

To identify the most important variables in a dataset, which is not their direct purpose

Question 32

Which of the following assumptions MUST be met for factor analysis to be considered valid?

Accepted Answer

The variables are continuous and approximately normally distributed.

Answer

The variables are not correlated.

Answer

The sample size is extremely large.

Question 33

What is the key difference between a factor loading and a communality in factor analysis?

Accepted Answer

A loading represents the correlation between a variable and a factor, while a communality shows the proportion of a variable's variance explained by all extracted factors.

Answer

A loading measures the importance of a variable, while a communality measures the reliability of a variable.

Question 34

When is factor analysis most appropriate to use in data analysis?

Accepted Answer

When you have a large number of correlated variables and want to simplify the data by reducing its dimensionality.

Answer

When you have a small number of uncorrelated variables and want to identify the most influential variables.

Question 35

What is the primary goal of factor analysis as a statistical technique?

Accepted Answer

To identify underlying factors that explain the relationships and variances observed in a set of variables.

Answer

To predict a continuous outcome variable based on multiple predictor variables.

Answer

To classify data points into distinct groups based on their similarities.

Question 36

Which of the following is NOT a core assumption of exploratory factor analysis?

Accepted Answer

The factors must be uncorrelated.

Answer

The sample size should be sufficiently large for reliable results.

Answer

There should be a linear relationship between the variables and the underlying factors.

Answer

The data should meet certain distributional assumptions (e.g., normality).

Question 37

In factor analysis, what does a high eigenvalue indicate about a factor?

Accepted Answer

The corresponding factor explains a large proportion of the variance observed in the original variables.

Answer

The factor is not statistically significant in explaining the data.

Answer

The factor loadings for that factor are weak and not very informative.

Question 38

Which rotation method in factor analysis is commonly used to achieve simple and interpretable factor loadings?

Accepted Answer

Varimax rotation

Answer

Equamax rotation

Answer

Promax rotation

Answer

Quartimax rotation

Question 39

What is the main purpose of using a scree plot in factor analysis?

Accepted Answer

To help determine the optimal number of factors to retain in the analysis, based on the 'elbow' in the plot.

Answer

To evaluate the strength of the relationships between the variables in the data.

Answer

To assess the normality of the data used in the factor analysis.

Question 40

In factor analysis, what do factor loadings represent in relation to the variables and factors?

Accepted Answer

The correlation between each variable and each factor, indicating the strength of their relationship.

Answer

The significance level of each factor in explaining the data.

Answer

The amount of variance explained by each factor in the analysis.

Question 41

How can factor analysis be leveraged to enhance the performance of machine learning models?

Accepted Answer

By reducing the dimensionality of the data and addressing multicollinearity, factor analysis can lead to simpler and more robust machine learning models.

Answer

Factor analysis can directly predict the target variable without the need for other features.

Question 42

What is the difference between exploratory and confirmatory factor analysis?

Accepted Answer

Exploratory factor analysis explores the underlying structure of the data, while confirmatory factor analysis tests a pre-defined factor structure.

Answer

Exploratory factor analysis is used for large datasets, while confirmatory factor analysis is used for small datasets.

Question 43

Which of the following is a potential limitation of factor analysis?

Accepted Answer

The interpretation of factors can be subjective.

Answer

It cannot handle datasets with a large number of variables.

Answer

It requires specialized software to perform.

Answer

It is not a widely used statistical technique.

Question 44

What is the relationship between principal component analysis (PCA) and factor analysis?

Accepted Answer

Both are dimensionality reduction techniques, but factor analysis aims to identify the underlying factors causing the correlations between variables, while PCA focuses on maximizing variance explained by components.

Answer

PCA is a type of factor analysis.