Can you post the raw data?

There are several ways for curve fitting, but I want to see what information can be extracted without applying any function at all (for example we can find the inflection point, if it is necessary).

Can you post the raw data?

There are several ways for curve fitting, but I want to see what information can be extracted without applying any function at all (for example we can find the inflection point, if it is necessary).

Theoretically the data should look like this (just the shape of course): http://webvision.med.utah.edu/imageswv/Kall04.jpeg

x values:

p = -10 -5 0 5 10

y values:

nanmean(TAS(:,:,2),2)' = 0.0550 0.1910 0.4420 0.7030 0.8190

nanmean(TBS(:,:,2),2)' = 0.0530 0.1980 0.5200 0.7510 0.8170

std of A und B data:

nanstd(TAS(:,:,2),1,2) = 0.1005 0.2208 0.3085 0.2199 0.1803

nanstd(TBS(:,:,2),1,2)' = 0.0654 0.2192 0.2467 0.2050 0.1683

In MATLAB:

x =[ -10 -5 0 5 10];

y1=[0.0550 0.1910 0.4420 0.7030 0.8190];

y2=[0.0530 0.1980 0.5200 0.7510 0.8170];

xx=[-10:0.01:10];

yy1=spline(x,y1,xx);

yy2=spline(x,y2,xx);

Result is pretty, see attachment.

If you could use R I could suggest you my package inflection:

http://cran.r-project.org/web/packages/inflection/index.html

see also my profile.

Then by using splines in R and with this package the inflection points are;

1st case=0

2nd case:

x_ese=-2.2

x_ede=-1.55

Continue the work and if you want to find inflection points ask me.

this looks really good. Thanks a lot.

PS: I have to stay inside Matlab, because this is just a small part of my analysis.

edit2:

CSS = ['-r'; '-b'; '-b'; '-k'; '-g'];

for spl = 1:4 % spline approximations

if spl == 1

xx = min(p):0.1:max(p); % fine structure

[~, sz_xx] = size(xx);

yy = zeros(4,sz_xx);

end

yy(spl,:) = spline(p,nanmean(TG1S(:,:,spl),2)',xx);

plot(xx,yy(spl,:),CSS(spl,:))

end

=> http://prntscr.com/2u0twv

looks like spline isn't the right way to get the curve shape in every case... :(

spline() always fits curve through all given data points, right? But polyfit doen't.

Is it possible to make any fitting function respect y value limits (min = 0 max = 1)?

@Daniel, do not use polyfit, it is not a good choice for your problem.

By the way, what is the purpose of the curve fitting here? The need for a good graphical presentation or you are searching for other curve properties, like inflection point and so?

Try with nlinfit. You can use it with your own function.

http://www.mathworks.es/es/help/stats/nlinfit.html

here's my new "concept"...

I'll try to but all this in a function for a shorter code in the main file where I'm using this and of course for other people ;)

So this attached file is just the most important code lines...

... and the screenshot (I cannot attach both to one answer :( )

@ Demetris, yes polynoms only look good if you're really lucky for this kind of data.

@Daniel, your approximations:

vq1 = interp1(nanmean(TG1S(:,:,1),2),p,0.5);

vq2 = interp1(nanmean(TG2S(:,:,1),2)',p,0.5);

are not good!

Try the values I gave you

Offset_50Proz_Punkt_1=0

Offset_50Proz_Punkt_2=-2.2 or -1.52

Why are they not good?

PS: This has to be dynamic, I cannot set the values for every case.

You compute them via an interpolation and this kind of computation is dangerous (see the polyfit discussion). You have to use a method to find the inflection point every time (of course, since it is dynamic).

but this just linear interpolates the x values at y=0.5. What's dangerous here? I'm using the raw data and no curve like polynom, spline. So I just get the value through nearest data points around and the straight line through them. Isn't this interp1(y,x,0.5)?

You can use whatever function you like and estimate regression parameters using fminsearch. You just have to build a cost function out of your data and pass that to the optimizer.

@Daniel, you wrote:

"So I just get the value through nearest data points around and the straight line through them"

It is simply not the best that you can do in order to find the inflection point Off50

Another issue is this: How are you sure that your curve is symmetric?

@ Demetris,

the curve has to be symmetric, because this data is gathered in a test of speech understanding in 4 different maskers (e.g. fastl noise) and the experience of many many year has show that this kind of data has that shape when you lot it with SNR = x-axis and understanding in % = y-axis.

Maybe this is not exactly a perfectly point symmetric curve around the Off50 point but it's very close to that.

What I thought about is that the gradient may be just a bit to low in my calculation.

I know that my linear interpolation of the 50% point is just an approximation, but a very good one as the curve's almost linear in this area. So let's try to build some fit2boltzmann()... (will post when it's ready)

@ David,

thanks a lot for this hint. I'll try to use this fminsearch() for boltzmann fit...

regards,

Daniel

@Daniel, can you provide me with a set of Boltzmann-like data?

I do not want to create random data, I'd prefer real data in order to study their Off50point and search some issues based on my research work.

Then we could probably compare the methods (the curve fitting and the non parametric).

How do you find this idea?

I additional approximated the maximal values. now it's ~95% (arithmetic mean of max. values (of all data I could find of the test persons))

PS: Sounds great. I just sent you some data...

@Daniel, your data seem not to fit a particular sigmoid pattern, if we classify them with independent variable the dB and dependent variables:

p1=m

p2= w

p3= r

p4= ref

See my attachment (red, green, black, blue-->p1,p2,p3,p4)

Thanks for the fitting, Demetris,

but this is the general spline problem as a lot of test persons score almost 100% at 5dB and at 10dB. In this area spline adds another inflection and spline also includes the given data points as part of the spline curve.

I sent you the mean, max, min values. Maybe this will help.

I think fitting the data to boltzmann function by using inflection point, gradient in inflection point and maximum score should result in better plots. Don't you agree?

So fminsearch should be the right choice. I never used this, did you? Are these three variables enough for fitting boltzmann with fminsearch?

Daniel, the situation is much better with mean values.

But I think it is not worth using splines, they destruct data.

See my plot with splines and the other with data only.

I use my package inflection for both cases.

I think you should use only mean values without splines.

Good luck

And the plot without splines here.

good, so back to the inflexion point / 50% = y value point: How would you interpolate it, if not linear out of nearest data points?

Daniel, please give me just one data set with your 4 or 6 exact points and mean value. There is a good chance that I can get a solution without splines. Answer would be made of just one soft curve function -somewhat complex- ; once done, proxy inflexion points might be estimated later by you. OK, emilio.