[BlindMath] Seeking Out Free-Access Accessible Statistics Resources

Fri Jul 20 06:53:54 UTC 2018

Hi Zac,

A broken stick model is just a piecewise linear function where the two line segments join at a single knot point. Left of the knot there is one slope that is different to the slope on the right. Sometimes the two segments are allowed to have a discontinuity instead of a knot (more like two sticks then).

If you know the likely place to put a knot, then the slope to the right of the knot point is modelled as a modification of the line left of it. This is just a change in slope for the data to the right of the knot. To do that, we add a new variable to the standard linear model. Y = a + bx + e.

Note that I'm using English letters for everything here to make subscripts unnecessary, and that e is the error term.

Take the x variable, and use it to make the new variable. Let's call it w here. There are several ways to make w, but it is the maximum of zero or (x-k) for all the data stored in x. The w variable is a measure of distance to the right of the knot point (k); if x is left of the knot, then it has zero rightness.   
Ultimately, you will fit the model y = a + bx + cw + e.
The change in slope is tested on the significance of the c parameter.

Life gets more challenging if you do not know the right value for the knot point. The old-fashioned method was to experiment. More sophisticated tools do exist (in R anyway) to help determine the placement of the knot. Minor suboptimal placement isn't going to matter much as it happens.

I think the bigger problem you have is that you're assuming the broken stick is appropriate for the data. Maybe it is, and at least by fitting one as described above, you'll find out one way or the other.

I suggest fitting a smoother to your data and finding a way to decide if it is sufficiently like a broken stick to pursue that model. There are lots of smoothing options to choose from; if you have enough data, the choice will be fairly immaterial. The challenge will be to find out how straight that smoothed relationship looks. I don't know if you have any means to emboss a graph of the smoothed data for yourself or if you'll need sighted assistance to make a call.

If plotting a smoothed set of data is beyond you, then go back to basics. Fit the straight line and check out the residuals from that model. The sign of the residuals for any given subset of data should be split 50-50 positive and negative. If sections within the range of the x variable do not have a roughly equal number of positive and negative residuals then there is a suggestion of nonlinearity to sort out.

Cheers,
Jonathan

-----Original Message-----
From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of Zach via BlindMath
Sent: Friday, 20 July 2018 12:35 PM
To: 'Blind Math list for those interested in mathematics' <blindmath at nfbnet.org>
Cc: Zach <zm290 at msstate.edu>
Subject: [BlindMath] Seeking Out Free-Access Accessible Statistics Resources

Hello: 

My knowledge of statistics for a masters student is laughable. My current thesis project, which happens to be in a subject area I hope to develop a career around, looks at the effect of various management practices and their relationship to mean farm milk quality parameters on Southeast dairy farms.
More specifically, I'm looking at the interaction these management practices have on milk quality in the presence of hyperthermia conditions. 

Multiple models for predicting hyperthermia from various  Meteorological parameters for various species of livestock at various stages of life have been developed using retrospective production records. Models specific to lactating dairy cows have been relatively well documented compared to other ruminant species. However, many of the models differ slightly on the inclusion and enthesis placed on parameters such as relative humidity, solar radiation, wind speed, black globe vs. wet bulb temperature, etc. What's more, several investigators use broken-line, linear, and nonlinear models to evaluate thermal neutrality. 

I am not experienced enough, and under enough pressure by my committee so I cannot perform a systematic review or meta-analysis, although I'd like to someday, to find the best model for my project. However, I was thinking of using a broken-line regression model, similar to the one employed by Hammami et al., (2013), to establish threshold values for hyperthermia using somatic cell count as my predictor variable. Would any one be able to suggest slightly more advanced tutorials accessible with JAWS V.17.0 I could access to try to help me? I have my committee members to guide me, but in order to really understand my statistical methods I need to read it to understand it.
I've attached a MS Word file (derived using OpenBook) as well as a MS Excel file with tables (from HTML version) from Hammami et al., (2013) if it helps. 

Any suggestions, comments, questions or concerns are all welcome. I know I've most likely put my foot in my mouth and misused some terminology and left out details that would help the gurus on this list to help me; and I humbly beg your forgiveness. If the files did not attach, please contact me off-list and I'll provide them. 

Kind regards,

Zac

Zachary Mason

M.S. Student

Animal and Dairy Sciences

Mississippi State University