Allowing users to insert additional fields

How can the form be set up so as to allow the respondent the ability to define a field a provide a rating in the matrix?  

I believe you are looking for Configurable List widget. The widget allows you to define the various field types per column on the list in a matrix-type of layout.

Please check this helpful guide: How-to-Set-Up-the-Configurable-List-Widget

Hope that helps. Thank you.

Somewhat Helpful but, not exactly what I was hoping for.  If you take a look at the form I am asking the respondent to rate various people on a 10-1 scale.  The form included a list of names to be rated.  I would like to invite the respondent to add names & ratings to the form in separate matrix (see end of form).  

Thank you for your assitance.

To my understanding, here's the field that you're trying to include to your form.

However, what you need to have is the ability for your respondents to add names and rate them similar to the other matrix in your form, is that correct?

Like what my colleague, Jan, have mentioned, what you need is the Configurable List widget. 

You just set the necessary fields that you need in the Configurable List widget's General tab.

Then, you add CSS codes to the widget's custom CSS tab, to make it look like the existing matrixes in your form.

Here's a sample that I have created: https://form.jotform.com/61205541995963

I would suggest you clone that form and inspect the Configurable List widget's General tab and Custom CSS tab.

Also, just a reference, you might want to check this guide for future references.

How-to-Set-Up-the-Configurable-List-Widget

I hope this helps. Let us know if you need any further assistance. Thank you.

Somewhat Helpful but, not exactly what I was hoping for.  If you take a look at the form I am asking the respondent to rate various people on a 10-1 scale.  The form included a list of names to be rated.  I would like to invite the respondent to add names & ratings to the form in separate matrix (see end of form).  

Thank you for your assitance.

On the form I have created above that has the Configurable List widget, respondents have the option to add names and rate them with a scale. However, all names will be on a single matrix.

Here's how it works:

Do you want each name to be added be in a separate matrix?

Can you help us by giving us more information or details of what you're trying to achieve, please, so we can further help you? 

We will wait for your response. Thank you.