Did you know that Power BI is an excellent interactive data visualization tool?

 Power BI is a business analytics tool developed by Microsoft. It provides interactive visualizations and business intelligence capabilities with an interface that is easy to use for creating reports and dashboards. Essentially, it turns our unrelated sources of data into coherent, visually immersive, and interactive insights. Whether our data is a simple Excel spreadsheet or a collection of cloud-based and on-premises hybrid data warehouses, Power BI lets us easily connect to our data sources, visualize (or discover) what’s important, and share that with others.

Here's a sample report I have produced using Power BI: 

Let's breakdown what Power BI is used for:

Data Connection: Power BI can connect to a wide range of data sources, including Excel files, databases, and cloud-based data, and it brings all the data together into a single view.

Data Transformation: Once the data is connected, Power BI allows users to transform and clean that data. Users can modify, aggregate, enhance, and clean the data as per the business requirements.

Data Visualization: Power BI enables users to create visualizations (like charts, graphs, and maps) and interactive dashboards. It provides a drag-and-drop functionality which makes creating reports and dashboards quite easy.

Data Analysis: With Power BI, users can explore data, discover patterns, and glean insights. The tool offers various analytics and artificial intelligence (AI) capabilities that can automatically spot patterns, help users understand what the data means, and predict future trends.

Data Sharing: After creating reports or dashboards, Power BI provides facilities to share the visualized data with others in the organization. This helps in making informed decisions by providing the right people with the right information.

Embedded Analytics: Power BI also allows users to embed analytics in an app or website for wider usage, extending its capabilities to more users.

Power BI helps us in our businesses to make data-driven decisions by enabling us to visualize and analyze our data in a more comprehensible and interactive way.

Download Power BI here: Power BI Desktop

Do you want to know why inflation is bad and why the Bank of England is rising interest rates?

Inflation refers to the rise in prices of goods and services over time. When inflation is high, your money doesn't go as far because everything gets more expensive. Imagine you could buy a loaf of bread for £1 last year, but this year it costs £1.20. That's because of inflation. If your wages or savings aren't increasing at the same rate as inflation, you'll find it harder to buy things or maintain your standard of living.

Inflation can be bad for several reasons:

• It reduces the purchasing power of money, meaning your money buys less.
• If it's unexpected, businesses might struggle to set the right prices for their products.
• People might delay spending because they expect prices to keep rising.
• If wages don't keep up with inflation, people might feel poorer and become less confident about the economy.

The Bank of England (and other central banks) has a tool to try and control inflation: interest rates. Here's how it works:

When the Bank of England raises interest rates, borrowing money becomes more expensive, and saving money becomes more attractive. If borrowing is more expensive, people and businesses might cut back on spending and borrowing. This reduced spending can slow down the economy a bit and, in turn, help reduce inflation.

On the other hand, when saving becomes more attractive because of higher interest rates, people might decide to save more and spend less. This again reduces the demand for goods and services, which can help to control rising prices.

So, the Bank of England raises interest rates to make borrowing less appealing and saving more appealing, which can help cool down an overheated economy and keep inflation in check.

A More Formal Presentation of Factor Analysis

In a previous post, a simplified overview of Factor Analysis was provided. In this one, I would like to present a more formal description of it.  

Note: You can download a pdf version of this article using the link provided below this post. 

In factor analysis, we have a set of observed variables, X_1,X_1,…,X_p, which we believe are linear combinations of underlying unobserved factors, F_1,F_2,…,F_m, plus some error term, ɛ. The error term accounts for all other unobserved variability in the X variables.

Mathematically, for each observed variable, we express it as:

X_i=a_i1 F_1+ a_i2 F_2+a_im F_m+ ɛ_i,i=1,2,...,p

Where: 

X_i = Observed variable

F_j = Unobserved latent factors

a_ij = Factor loadings of factor j on variable i

ɛ_i = Unique variance (error term) associated with variable 

p = Total number of observed variables

m = Number of factors

Observed Variables (X_i): The actual data you have—like scores on a test, economic indicators, etc.

Unobserved Latent Factors (F_j): Variables not directly observed but inferred from the mathematical model. These capture the underlying processes or constructs that might explain the patterns in your data.

Factor Loadings (a_ij): These are the coefficients which indicate the degree to which each X_i is influenced by each F_j. Factor loadings are akin to weights, showing the impact of factors on the observed variables.

Error Term (ɛ_i): This represents the portion of variability in X_i that cannot be explained by the common factors.

Factor Extraction and Retention:

Factor extraction typically begins with calculating the covariance or correlation matrix of the observed variables. Eigenvectors and eigenvalues of this matrix are computed to determine the factors and how much variance each factor explains. The number of factors to retain might be determined using various criteria, such as Kaiser’s criterion (eigenvalue > 1) or the scree plot method.

Example in Econometrics:

Imagine an economist is looking at variables like GDP growth, unemployment rate, inflation rate, and interest rates (X_1,X_1,…,X_p) and hypothesizes that they are influenced by underlying, unobserved factors like economic stability and monetary policy (F_1,F_2).

GDP Growth=a_11 F_1+a_12 F_2+ɛ_1  

Unemployment Rate=a_21 F_1+a_12 F_2+ɛ_2

Inflation Rate=a_31 F_1+a_32 F_2+ɛ_3

Interest Rate=a_41 F_1+a_42 F_2+ɛ_4

The task is then to use the observed data to estimate the factor loadings (a_ij) and deduce the nature of the latent factors. This often involves rotation methods to make the solution more interpretable.

Factor analysis provides a robust technique for economists, and others, to explore and understand the dimensional structure of observed variables, providing insight into unseen influences in their data. While the math can be complex, the foundational understanding remains rooted in identifying and understanding these underlying, latent factors.

If you are keen to read more on factor analysis, please check out these books: 

Factor Analysis: Statistical Methods and Practical Issues by Jae-On Kim and Charles W. Mueller. This book provides a comprehensive overview of factor analysis and is widely respected in the field.

Applied Multivariate Statistical Analysis by Richard A. Johnson and Dean W. Wichern. This book covers a variety of multivariate techniques, including factor analysis, and is quite accessible for various skill levels.

A Handbook of Statistical Analyses using SPSS by Sabine Landau and Brian S. Everitt. Though software-specific, this handbook presents the application of numerous statistical methods, including factor analysis, using practical examples.

Sorry for the poor presentation of variables and equations. It is because Blogger does not support math language the way we type them in Microsoft Word or LaTeX. If you would like to see and read the equations and variables in a nice and neat shape, please download a pdf version of this article using the following link: A More Formal Presentation of Factor Analysis

Factor Analysis: A Simplified Overview

Factor Analysis is a statistical technique that we use to identify underlying relationships between different variables. Imagine we have a lot of related variables, and we suspect that these could be influenced by a few underlying factors. Factor analysis helps us to unearth these underlying factors.

                                                        Diagram source: Statistics By Jim

Basic Concept:

Think of factors as underlying (and unobservable) variables that somehow influence the observable variables we measure directly. Factor analysis tries to find out how many of these hidden factors might be influencing the patterns of response we see in our data and what variables are related to which underlying factor(s).

Example:

Imagine we are researching why students get the grades they do. We have data on various variables, such as attendance rate, hours spent studying, sleeping hours, part-time job hours, and so forth. These variables can be many and somewhat overwhelming to analyse individually.

Let’s dive a bit into the example:

Identifying Factors: We hypothesize that these observable variables (e.g., study hours, sleep hours) might be influenced by a few unobservable factors like Work Ethic or Time Management.

The Relationship:

Maybe hours spent studying and attendance rate are both influenced by an underlying factor we might label as Diligence.

While sleeping hours and part-time job hours might be influenced by Time Management.

Why bother?

It helps us reduce our workload: Instead of dealing with 5, 10, or 50 variables, we can group them under a few factors and work with those, making our analysis more straightforward and interpretable.

It provides insight into the patterns or structures (the underlying factors) in our data: We can understand what hidden influences might be driving the observable patterns in our data.

Steps in Factor Analysis:

Extraction: Extract the minimum number of factors that can aptly represent the patterns in the relationship among variables.

Rotation: Rotate the factors to ensure that they make sense (both statistically and theoretically). Rotation can help simplify and interpret the data.

Interpretation: Assign labels to the factors (like 'Diligence' or 'Time Management' in our example) and interpret the data accordingly.

Application:

Once the factors are identified and interpreted, we can:

·       Use them to understand how different variables interact.

·       Develop strategies (like study plans or interventions) that target the underlying factor, affecting all associated variables simultaneously.

To sum-up, Factor Analysis simplifies data by finding the unobservable factors influencing the patterns of observed variables, aiding in data interpretation and strategy formulation, especially when dealing with numerous variables.