Which modeling technique is commonly used for analyzing complex and multi-dimensional data in data warehousing?

The modeling technique commonly used for analyzing complex and multi-dimensional data in data warehousing is called "Online Analytical Processing" or OLAP.

Here are the steps to explain how it works:

1. Data Collection: The first step in the OLAP analysis is the collection of data from different sources. This data is usually raw and unprocessed, collected from various operational databases.

2. Data Integration: The next step is to integrate the collected data. This involves combining data from different sources and providing a unified view of the data.

3. Data Cleaning: After integration, the data is cleaned. This step involves removing or correcting any inaccuracies in the data, removing duplicates, and dealing with missing values.

4. Data Transformation: The cleaned data is then transformed into a suitable format for the OLAP analysis. This could involve operations such as aggregation, summarization, or any other mathematical computation.

5. Data Loading: The transformed data is then loaded into an OLAP cube. An OLAP cube is a multi-dimensional array of data that allows for complex analytical and ad-hoc queries with a rapid execution time.

6. Data Analysis: Finally, the data in the OLAP cube is analyzed. This could involve operations such as drilling down into the data to view more detailed information, rolling up the data to view aggregated information, slicing the data to view a subset of the data, and dicing the data to view the data from different perspectives.

So, OLAP is a powerful tool for data analysis in data warehousing, allowing users to perform complex calculations and view data from various perspectives.