fitting - Keeping Nonlinear Model Fit Real

So I am using the NonlinearModelFit (NLM) command with a fairly simple function. There are 4 unknowns and the (x, y) points that I am fitting the function to. I am getting my approximations from a Manipulate so I can just tweak the values till it's close enough. But once I get the values into the NLM, I get this error about the function value not being a real number at these values (not the same values that I put into the NLM). I have tried several different sets of values and every time I get the same error. I do have two constraints that keep two of my values positive.

R = 0.42; Sigma = 73.06967052; Theta=1.32757;

nData={{0.989939, 4.62}, {0.989939, 4.64}, {0.989939, 4.66},
       {0.989939, 4.68}, {0.989939, 4.7}, {0.989939, 4.72},
       {0.989939, 4.74}, {0.989939, 4.76}, {0.989939, 4.78},
       {0.989939, 4.8}, {0.99398, 4.82}, {0.99398, 4.84},
       {0.99398, 4.86}, {0.99398, 4.88}, {0.99398, 4.9},
       {0.99398, 4.92}, {0.99398, 4.94}, {0.99398, 4.96},
       {0.99398, 4.98}, {0.99398, 5}, {0.99398, 5.02},
       {0.99398, 5.04}, {0.99398, 5.06}, {0.99398, 5.08},

       {0.99398, 5.1}};

nlm = NonlinearModelFit[
    nData, 
    {((3 + s)/(1 + s) 1/R (h + dh)^(1 + s))* ((p/(Sigma*Cos[Theta]))^s)*
        Hypergeometric2F1[1 + s, s, 2 + s, (h + dh)/h0], s > 0, p > 0}, 
    {{p, 0.207}, {s, 1}, {h0, 2.04}, {dh, 0.9}}, h
 ]

Comments

plotting - Filling between two spheres in SphericalPlot3D

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plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1.

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