# Searching for appropriate statistical model

• aardflouf
In summary: Another option could be to use a generalized additive model (GAM) which can handle non-linear relationships and can incorporate constraints. In summary, there are several mathematical models that could potentially fit this type of data, such as polynomial regression, spline regression, loess regression, and generalized additive models (GAM). It may require some experimentation to determine which model best fits the data and achieves your goal of describing the top edge of the depth vs diameter plot.
aardflouf

## Homework Statement

Hello, I'm looking for direction in finding whether any mathematical models exist for a specific type of trend.

I've created a blog for an online class and have started looking at Mars crater data. The graph below appears to have a maximum value for depth as diameter increases. My goal is to apply a statistical model that describes the top edge of the depth vs diameter plot.

Applying linear regression would not be appropriate in this case, since I'm interested in the edge of the data, not its lower values.

Does a model exist for fitting this type of data?

## Homework Equations

Y = a1*x1 + a2*x2 + ... + an+xn + e
doesn't seem to apply here.

I'm looking for something like:
maximum(Y) = a1*x1 + a2*x2 + ... + an+xn + e
or
Y <= a1*x1 + a2*x2 + ... + an+xn + e

## The Attempt at a Solution

One option is to write a program that picks the top n values for each increment along the x-axis (diameter), but this would not provide reproducible results, and would be too sensitive to outliers.

I've searched for:
• inequality-constrained linear models
• boundary models
• linear threshold model

none of these were insightful. is anyone familiar with models that would be appropriate for this type of data?

A possible solution could be to use a non-linear regression model such as polynomial regression or spline regression. These models can capture the shape of the data more accurately than a linear regression model, and can account for the edge of the data as well. You could also try using a smoothing technique such as loess regression.

## What is the purpose of searching for an appropriate statistical model?

The purpose of searching for an appropriate statistical model is to find the best way to analyze and interpret data in order to answer a specific research question or hypothesis. A statistical model helps to determine the relationship between variables and make predictions based on the data.

## What are the steps involved in searching for an appropriate statistical model?

The steps involved in searching for an appropriate statistical model include identifying the research question, selecting the appropriate variables, choosing the appropriate type of data, selecting the appropriate statistical test or model, and interpreting the results.

## How do I know which statistical model is the most appropriate for my data?

The most appropriate statistical model for your data depends on the type of data you have, the research question you are trying to answer, and the assumptions and limitations of the different statistical models. It is important to carefully consider these factors before selecting a statistical model.

## What are some common mistakes to avoid when searching for an appropriate statistical model?

Some common mistakes to avoid when searching for an appropriate statistical model include using the wrong type of data, misinterpreting the results, not considering the assumptions and limitations of the statistical model, and failing to properly address confounding variables.

## Can I use more than one statistical model to analyze my data?

Yes, it is possible to use more than one statistical model to analyze your data. This can be helpful in confirming the results and increasing the confidence in your findings. However, it is important to be cautious when using multiple statistical models and to clearly justify why they were chosen.

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