Statistical Modeling Definition

Statistical modeling is the use of mathematical models and statistical assumptions to generate sample data and make predictions about the real world. A statistical model is a collection of probability distributions on a set of all possible outcomes of an experiment.

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FAQs

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What is Statistical Modeling?

Statistical modeling refers to the process of applying statistical analysis to datasets. A statistical model is a mathematical relationship between one or more random variables and other non-random variables. The application of statistical modeling to raw data helps data scientists approach data analysis in a strategic manner, providing intuitive visualizations that aid in identifying relationships between variables and making predictions.

Common data sets for statistical analysis include Internet of Things (IoT) sensors, census data, public health data, social media data, imagery data, and other public sector data that benefit from real-world predictions.

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Statistical Modeling Techniques

The first step in developing a statistical model is gathering data, which may be sourced from spreadsheets, databases, data lakes, or the cloud. The most common statistical modeling methods for analyzing this data are categorized as either supervised learning or unsupervised learning. Some popular statistical model examples include logistic regression, time-series, clustering, and decision trees. 

Supervised learning techniques include regression models and classification models:

• Regression model: a type of predictive statistical model that analyzes the relationship between a dependent and an independent variable. Common regression models include logistic, polynomial, and linear regression models. Use cases include forecasting, time series modeling, and discovering the causal effect relationship between variables.
• Classification model: a type of machine learning in which an algorithm analyzes an existing, large and complex set of known data points as a means of understanding and then appropriately classifying the data; common models include models include decision trees, Naive Bayes, nearest neighbor, random forests, and neural networking models, which are typically used in Artificial Intelligence.

Unsupervised learning techniques include clustering algorithms and association rules:

• K-means clustering: aggregates a specified number of data points into a specific number of groupings based on certain similarities.
• Reinforcement learning: an area of deep learning that concerns models iterating over many attempts, rewarding moves that produce favorable outcomes and penalizing steps that produce undesired outcomes, therefore training the algorithm to learn the optimal process.

There are three main types of statistical models: parametric, nonparametric, and semiparametric:

• Parametric: a family of probability distributions that has a finite number of parameters.
• Nonparametric: models in which the number and nature of the parameters are flexible and not fixed in advance.‍
• Semiparametric: the parameter has both a finite-dimensional component (parametric) and an infinite-dimensional component (nonparametric).

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How to Build Statistical Models

The first step in building a statistical model is knowing how to choose a statistical model. Choosing the best statistical model is dependent upon several different variables. Is the purpose of the analysis to answer a very specific question, or solely to make predictions from a set of variables? How many explanatory and dependent variables are there? What is the shape of the relationships between dependent and explanatory variables? How many parameters will be included in the model? Once these questions are answered, the appropriate model can be selected. 

Once a statistical model is selected, it must be built. Best practices for how to make a statistical model include:

• Start with univariate descriptives and graphs. Visualizing the data helps with identifying errors, understanding the variables you’re working with, and how they look.. 
• Build predictors in theoretically distinct sets first in order to observe how related variables work together. Then the outcome once the sets are combined.
• Run bivariate descriptives with graphs in order to visualize how each potential predictor relates individually to the others and the outcome. 
• Frequently record, compare and interpret results from models run with and without control variables. 
• Eliminate non-significant interactions first; any variable involved in a significant interaction must be included in the model by itself.
• While identifying the many existing relationships between variables, and categorizing and testing every possible predictor, be sure not to lose sight of the research question.

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Statistical Modeling vs Mathematical Modeling

Much like statistical modeling, mathematical modeling translates real-world problems into tractable mathematical formulations whose analysis provides insight, results and direction useful for the originating application. However, unlike statistical modeling, mathematical modeling involves static models that represent a real-world phenomenon in mathematical form. Once a mathematical model is formulated, it does not necessitate change. Statistical models are flexible and, with the aid of machine learning, can incorporate new, emerging patterns and trends, and will adjust with the introduction of new data.

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Machine Learning vs Statistical Modeling

Machine learning is a subfield of computer science and artificial intelligence that involves building systems that can learn from data rather than explicitly programmed instructions. Machine learning models seek out patterns hidden in data independent of all assumptions, therefore predictive power is typically very strong. Machine learning requires little human input and does well with large numbers of attributes and observations.

Statistical modeling is a subfield of mathematics that seeks out relationships between variables in order to predict an outcome. Statistical models are based on coefficient estimation, are typically applied to smaller sets of data with fewer attributes, and require the human designer to understand the relationships between variables before inputting.

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Statistical Modeling Software

Statistical modeling software are specialized computer programs that help gather, organize, analyze, interpret and statistically design data. Advanced statistics software should provide data mining, data importation, analysis and reporting, automated data modeling and deployment, data visualization, multi-platform support, prediction capabilities, and an intuitive user interface with statistical features ranging from basic tabulations to multilevel models. Statistical software is available as proprietary, open-source, public domain, and freeware.

1. Starting early ignites a lifelong love of learning

STEM teaches kids so much about the world. It opens their minds and they start asking questions about why things are being done. STEM teaches them things they are interested in like how their favorite video game works! There is so much to learn and explore!

2. STEM builds the skills kids need for the future

Did you know that there are already 600,000 unfilled positions in the tech sector? About 65% of children will be working in jobs that don’t exist yet and that gap will only grow. A STEM education ensures that the children today will have all the tools they need to create a better future!

3. Learning on their own terms

One of the biggest advantages of STEM is that kids learn to solve problems. They are driven by their interests which allows them to learn to problem solve without them ever feeling like they are in school. By putting the kids in the driving seat of their learning, they think critically about their own ways to solve problems they face.

4. Tech will save us

STEM is at the heart of empowering kids. There is so much to be invented and explored and what better way than to start children early in STEM? Like we said before, STEM is only growing and will continue to grow. Not only will there be plenty of high starting pay jobs, but they will also have a lifelong time of learning.

STEM education is more critical than ever. We are only at the beginning of the digital age. This has made science, technology, engineering, and mathematics education more important than ever. Early STEM education can promote ongoing academic success. Children who learn STEM concepts throughout their education are better prepared to meet increasingly technology-focused professional requirements.

STEM concepts help children develop new ways of thinking, encouraging curiosity and analysis. Establishing these at an early age when young minds are most workable, establishes lifelong thinking skills. Early age is typically infancy through third grade. 

STEM also helps children with other fields of study. Research has shown a link exists between science instruction and improvement in literacy, language learning, and executive functioning. Students who engage with STEM subjects gain skills that better prepare them for technology-focused roles. When teaching young children STEM education, it is not dependent on digital technology. For example, block play, gardening, and puzzles are examples of STEM education. Even visits to museums can be considered STEM education. 

Parents who are aware of the benefits of a STEM curriculum are more likely to be supportive of STEM education. They are also more likely to encourage activities at home that develop STEM concepts. The belief that STEM is for older students has contributed to younger grades not being funded as much as higher grade levels. People need to start introducing STEM to kids at a young age. 

A study by researchers at the University of California Irvine found that early math skills were the most consistently predictive measure of future academic success among kindergarten to fifth-grade students.

Research supported by the National Science Foundation concludes that young children benefit from learning STEM subjects, which include Science, Technology, Engineering, and Math, because these disciplines play a fundamental role in setting the foundations for future learning.

STEM and Language Development

STEM education and activities are thought to play a key role in the acquisition of language skills. For example, when kids read books about technology or science, it can spark curiosity in them. And what they’ve read may prompt children to plan and carry out an investigation to test a hypothesis, which is a crucial aspect of a scientific investigation.

Children would then be encouraged to discuss their hypotheses and results with each other. This then develops literacy and comprehension skills.

STEM Encourages Independent and Collaborative Learning

As the report highlights, STEM education allows children to develop their communication and problem-solving skills. When kids are actively encouraged to talk and write about their ideas and observations, this helps their problem-solving skills tremendously. This enables young children to develop concepts through investigative and explorative means.

Young children benefit from a STEM education because they are typically naturally curious and want to explore and make sense of the things around them. Young children who are non-native. English speakers can also benefit from a STEM education because they can participate in scientific explorations that do not demand an extensive vocabulary.

STEM in Practice

This report recommends that children should be introduced to these subjects before kindergarten. Teachers should then dedicate enough time to give students quality STEM learning until the third grade, at least. Teachers should establish and promote STEM ways of thinking. Also, there should be opportunities to read, write, and discuss those subjects in detail. Teaching kids STEM early, allows them to make connections between their everyday life and STEM disciplines. It also gives the children transferable skills to other subjects.

Learning Through Self Discovery

There are a few things parents can do to ensure their children are being exposed to STEM at home. They can do this by encouraging independent thinking by making connections between their experiences at school and home.

An easy and efficient way to do this is to simply ask a child what they learned in their science class that day or week. This will help them to consolidate that learning experience as they explain and discuss the topic. If you want to take it one step further, parents can encourage their children to undertake a mini project relating to the topic at home. This encourages independent thinking. This shows the kid that STEM is not only learned at school and may spark their curiosity even more.

Make sure your children are introduced to the benefits of STEM education at school and at home!  

STEM subjects are so broad and cover a vast range of studies. Here are a few areas where your STEM education can take you.

As a math tutor, I have lots of experience helping students who are struggling to increase their math confidence. I’ve found that these students decide early on that “math just isn’t my thing”, but nothing could be further from the truth. The real struggle, I think, has much more to do with a lack of math confidence when it comes to problem-solving.

When you think about a math problem, there are so many places mistakes can be made. Not only do you have to know all the steps, but you have to know the correct order of those steps, as well as how to execute each one without making any mistakes. A lot is riding on it, so students understandably get frustrated and quickly lose confidence if things aren’t going their way.

How can you avoid the frustration and maintain self-confidence? Below are some of the techniques I use.

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1. TRY THE QUESTION YOURSELF.  I always like it when the students try a problem first, and then ask me how to do it as a last resort. When they attempt it alone, more often than not, they know what to do – they just need an expert or a tutor to be with them to assure them they’re doing it the right way. Receiving instant expert feedback is good for diagnosing where the issue is in their understanding of the concept, and it also provides positive reinforcement. Everyone likes being told they’re doing a good job, right? It is also important that the feedback be descriptive. The more descriptive it is, the quicker the students will come to see exactly what made them successful. This builds math confidence.
2. WALK THROUGH IT STEP-BY-STEP.  Typically, before doing any of the actual homework problems, I will give students a couple of examples similar to the ones they’ve brought in. We walk through them together step-by-step, and as we break it down, I ask them, “So what do you want to do here?” and “Why do you want to do that?” By having them explain their thought process, they start to see where the holes in their understanding are. As the holes get filled, their math confidence improves. This leads me to…
3. TEACH SOMEONE ELSE.  This is my favorite way to build math confidence. Explaining helps immensely with understanding. If students are missing certain foundation elements, that will hinder their future learning and prevent them from mastering any new material that comes up in school. If your student is struggling, sit down with them and ask them to explain some problems to you as if you were learning the material for the first time. When they are forced to break a problem down into its simplest terms, it reinforces those foundation concepts that are so important.
4. LEARN SHORTCUTS.  Another effective approach is teaching shortcuts. Kids come in all the time complaining about solving problems that are not inherently difficult, but are made so because they have a rigid approach to problem-solving – an inability to see the problem from a different perspective. They know only one route to the solution. Math is very flexible though, and when students learn there are multiple ways to solve a problem, it becomes much more enjoyable. If one method doesn’t work, they can always try another.
5. LEARN THE APPLICATIONS.  Something many teachers fail to do for their students is teaching them how to apply what they are learning to the “real world.” I dread being asked, “When am I ever going to use this in my life?” (even though I know I asked it many times myself). As I said earlier, math is very flexible. If you look hard enough, you can find it anywhere. As students advance in their mathematics education, they will undoubtedly find that most of the material they learn in school is not used by the general population. BUT…the whole reason we learn math in school is to improve our ability to solve problems. We solve problems every day, but mathematics is just a formal, algorithmic way of doing it. Math is so much more interesting when you realize how much of your life is determined by underlying equations and formulas.
6. PRACTICE.  Last but not least, practice. Students don’t like it, but this is the single best way to increase math confidence. Students can listen to lectures all day long, but there’s really no way to test their knowledge aside from applying it to actual problems. To be good at math, just like anything, you have to practice every day. Spending an extra 20 minutes each day doing practice problems – or supplementing the school lectures with videos on sites like Khan Academy – add up to almost two and a half hours per week. Students will feel more prepared for tests and quizzes, and feeling prepared is vital to increasing confidence. The extra practice will pay dividends over time in the form of better grades, better test scores, and more scholarship money.

As far as confidence goes, there is no substitute for feeling prepared and being self-reliant. However, if your child is struggling in math (or any subject), consider finding a tutor who can give a boost to their self-esteem.