[R-sig-eco] Relationship between x and latitude

[Zoltan Botta-Dukat]

Dear Peter,

Looking the figure I think not average of x, rather its maximum change 
with the distance from the equator.
You could try the quantile regression (quantreg package) developed to 
such cases. An introduction to this method for ecologists can be 
downloaded from here:
http://www.econ.uiuc.edu/~roger/research/rq/QReco.pdf

Best wishes

Zoltan



2011.01.25. 15:51 keltezéssel, Peter Francis írta:
> Dear List,
>
> I am looking at the relationship between a quantity and the distance from the equator.
>
> Asking the question does latitude effect the value of x - i.e is x higher or lower as you move away from the equator
>
> I have plotted x against latitude(plot(latitude,x))  and there seems to be something there, however i was wanting to investigate in a more quantitative way. I had thought of models but my experience is relatively low and i am unsure what method would be best for my pattern of data. Any advice would be greatly appreciated.
>
> ###data###
> x<-
> c(0.015348175, 0.014102894, 0.013158871, 0.012796208, 0.012547266,
> 0.012499614, 0.011580142, 0.011274077, 0.011026623, 0.010934845,
> 0.010866659, 0.01075808, 0.010581273, 0.010548757, 0.010415088,
> 0.010395809, 0.010328903, 0.009754356, 0.009652272, 0.009533795,
> 0.009179444, 0.009141853, 0.009140609, 0.008882345, 0.008671247,
> 0.008426542, 0.008407421, 0.008248698, 0.008228469, 0.008169984,
> 0.008158929, 0.007978867, 0.007893121, 0.007886193, 0.007785512,
> 0.007613687, 0.007591255, 0.007542375, 0.007532009, 0.007497797,
> 0.007487081, 0.007469353, 0.007369905, 0.007169296, 0.007122561,
> 0.007070457, 0.006975594, 0.006948638, 0.006805148, 0.006791063,
> 0.006783499, 0.006733242, 0.006733242, 0.006701148, 0.006691116,
> 0.006672124, 0.006660939, 0.006571554, 0.006552405, 0.006536592,
> 0.006523875, 0.006480761, 0.006471293, 0.006454864, 0.006365157,
> 0.006356432, 0.006323978, 0.006260515, 0.006188042, 0.006187938,
> 0.006181114, 0.006181114, 0.006079529, 0.006017497, 0.006008061,
> 0.005953895, 0.005920824, 0.005899296, 0.00589274, 0.005862688,
> 0.005853862, 0.005811885, 0.005778694, 0.005736366, 0.005686819,
> 0.005686362, 0.005621206, 0.005607628, 0.005567988, 0.005532497,
> 0.005493249, 0.005433072, 0.005429215, 0.005420174, 0.005408397,
> 0.005382781, 0.005304967, 0.005298177, 0.005273268, 0.005158224,
> 0.005135415, 0.005092708, 0.005048508, 0.005048015, 0.005044948,
> 0.005028163, 0.005028163, 0.005014717, 0.004967595, 0.00489943,
> 0.004887419, 0.004887419, 0.004887419, 0.004861756, 0.004842995,
> 0.00476598, 0.004734517, 0.004689229, 0.004657052, 0.004624096,
> 0.004618037, 0.00460988, 0.004606092, 0.004531219, 0.004527051,
> 0.004506577, 0.004482963, 0.004476035, 0.004476035, 0.004476035,
> 0.004476035, 0.004476035, 0.004419306, 0.004413048, 0.004366397,
> 0.00434048, 0.00434048, 0.004302982, 0.004296803, 0.004290441,
> 0.004285631, 0.004275535, 0.004254518, 0.004207445, 0.004173182,
> 0.004155142, 0.004134336, 0.004110218, 0.004106806, 0.004105657,
> 0.004091356, 0.004018147, 0.004003681, 0.003994852, 0.003993325,
> 0.003983061, 0.003966886, 0.003918854, 0.003917177, 0.003891429,
> 0.003842899, 0.003842899, 0.003834539, 0.003832233, 0.003818814,
> 0.003789309, 0.003707218, 0.003697771, 0.003668882, 0.003668882,
> 0.003602582, 0.003602582, 0.003602582, 0.003591953, 0.003537737,
> 0.003513987, 0.003464507, 0.003459366, 0.003437983, 0.003400975,
> 0.003377825, 0.003366575, 0.003285648, 0.003270708, 0.003260783,
> 0.00318234, 0.00318234, 0.003151494, 0.0031, 0.003094114, 0.003082046,
> 0.003081427, 0.003069106, 0.003069106, 0.003052216, 0.003036596,
> 0.003035941, 0.003032508, 0.003023303, 0.003020964, 0.003019848,
> 0.002981245, 0.002978949, 0.002969224, 0.002958385, 0.002955199,
> 0.002954933, 0.002954933, 0.002950752, 0.002918346, 0.002906109,
> 0.002902979, 0.002901011, 0.002896504, 0.002877516, 0.002849816,
> 0.002843091, 0.002828998, 0.002817939, 0.002816043, 0.002803956,
> 0.002798723, 0.002790437, 0.002777884, 0.002777884, 0.002777884,
> 0.002777884, 0.002777884, 0.002777884, 0.002777884, 0.002777555,
> 0.002776965, 0.002771398, 0.002752354, 0.00272757, 0.002717057,
> 0.002701395, 0.002687727, 0.002635401, 0.002635401, 0.002635401,
> 0.002635401, 0.002631182, 0.002623146, 0.002616387, 0.002584465,
> 0.002578125, 0.002577877, 0.002548996, 0.002488092, 0.002476084,
> 0.002474694, 0.002451195, 0.002443587, 0.002442069, 0.002439442,
> 0.002439442, 0.002425784, 0.002418847, 0.002409969, 0.002404593,
> 0.002401727, 0.002401727, 0.002401727, 0.002400578, 0.002364737,
> 0.00235511, 0.002326208, 0.002326208, 0.002323944, 0.002317546,
> 0.002275955, 0.002261807, 0.002219485, 0.002217373, 0.002210748,
> 0.002208339, 0.002199135, 0.002192113, 0.002171856, 0.002171856,
> 0.002156217, 0.002126684, 0.002090031, 0.002086738, 0.002086209,
> 0.002078779, 0.002047235, 0.002040628, 0.002036937, 0.002036773,
> 0.002036773, 0.002017393, 0.002009864, 0.001999733, 0.001998787,
> 0.001990045, 0.001986944, 0.001975691, 0.001971625, 0.001945183,
> 0.001936149, 0.001926163, 0.001919142, 0.001897503, 0.001897503,
> 0.001887366, 0.001866615, 0.001865528, 0.001860441, 0.001851106,
> 0.001850471, 0.001807395, 0.001807281, 0.001794796, 0.001790554,
> 0.001778587, 0.001773777, 0.001770118, 0.001726876, 0.001716987,
> 0.001705133, 0.001692117, 0.001675794, 0.001605834, 0.001605667,
> 0.001598937, 0.001575879, 0.001565384, 0.001546179, 0.001534643,
> 0.001525447, 0.001522089, 0.001502833, 0.001481944, 0.001473202,
> 0.001452109, 0.001449217, 0.001446246, 0.001446246, 0.001422652,
> 0.001422652, 0.001375286, 0.001361211, 0.001356151, 0.001347116,
> 0.001339627, 0.001339627, 0.00133279, 0.001331517, 0.001331517,
> 0.001331517, 0.001331517, 0.001322368, 0.001306458, 0.001296254,
> 0.001257304, 0.001238302, 0.001238302, 0.001238302, 0.001223937,
> 0.001191425, 0.001189038, 0.001180128, 0.001176136, 0.001144119,
> 0.001122304, 0.001109047, 0.001072805, 0.001072805, 0.001072805,
> 0.001072805, 0.001072805, 0.001072805, 0.001072805, 0.001072805,
> 0.001072805, 0.001072805, 0.001072805, 0.001072805, 0.001072805,
> 0.001072805, 0.001072805, 0.001072805, 0.001072805, 0.001072805,
> 0.001072805, 0.001072805, 0.001060498, 0.001051146, 0.001051146,
> 0.001015594, 0.000997827, 0.000979584, 0.000979125, 0.000959362,
> 0.000932058, 0.000927945, 0.000927867, 0.000909772, 0.000898857,
> 0.000891068, 0.000816096, 0.000804403, 0.000783013, 0.000781831,
> 0.000750918, 0.000744673, 0.000739314, 0.000738508, 0.000735344,
> 0.000712073, 0.000679757, 0.000679757, 0.000674523, 0.000636956,
> 0.000629264, 0.000623775, 0.000621972, 0.000620247, 0.000617503,
> 0.000615432, 0.000580207, 0.000548295, 0.000540084, 0.000527764,
> 0.000518084, 0.000510753, 0.000507758, 0.000493544, 0.000490135,
> 0.000468122, 0.000468122, 0.000466777, 0.000440226, 0.000420408,
> 0.000409094, 0.000393234, 0.000373562, 0.000373562, 0.000373562,
> 0.000373562, 0.000373562, 0.000373562, 0.000373562, 0.000373562,
> 0.000347605, 0.000344458, 0.000343825, 0.000335533, 0.000315615,
> 0.000313374, 0.000313148, 0.000246113, 0.000239747, 0.000227964,
> 0.000224992, 0.000215867, 0.000197565, 0.000196167, 0.000171385,
> 0.000170994, 0.000156109, 0.000129517, 0.000126808, 0.000126808,
> 9.35e-05, 6.5e-05, 6.5e-05, 5.95e-05, 5.59e-05, 4.36e-05, 4.36e-05,
> 4.36e-05, 3.74e-05, 3.34e-05, 2.14e-05, 2.02e-05)
>
> latitude<- c(4.845, -21.9, 6.395, 19.79, 5.385, -25.565, -27.83, 19.93,
> -10.995, 6.255, 7.035, 2.51, 15.16, 20.985, -29.59, -10.12, 27.655,
> 14.405, -0.165, 24.04, 20.765, -12.385, -12.03, 9.955, 11.46,
> 3.425, 1.01, -4.22, 12.52, 36.325, 8.46, 22.655, 15.11, 41.925,
> 34.395, 12.12, -30.375, -0.535, 17.47, -11.415, 30.11, 4.84,
> -32.045, -18.435, 36.37, 20.55, 2.395, 1.895, -1.17, 35.7, 24.72,
> -1.365, -1.035, 37.045, 17.745, 0.955, -15.34, 4.65, -22.675,
> -34.015, -23.56, 39.615, -4.415, 28.98, 36.96, 16.39, 41.26,
> -0.75, 18.58, 4.395, -32.605, -0.365, 4.975, -17, 40.67, 7.43,
> 5.07, 2.125, 1.25, 21.28, 3.695, -6.16, 11.13, -35.655, 21.905,
> 10.54, 5.145, 1.615, 10.29, 13.345, 42.71, 10.405, 39.17, -6.625,
> 7.845, 19.115, 23.295, 18.065, 7.31, -5.53, 56.1, 10.23, -25.705,
> 44.31, 17.135, -20.11, -6.87, -5.21, 15.635, -11.675, -46.71,
> 39, 42.845, -11.505, 18.855, -6.895, 29.55, 11.865, 16.875, -32.09,
> -14.44, 32.46, 33.49, -11.655, 7.275, -12.305, -3.35, -34.16,
> -3.855, 33.455, 38.615, 54.455, 10.63, 30.775, 37.525, 25.325,
> 30.935, 43.085, 7.69, -2.235, 11.225, 10.51, 22.26, 9.005, 40.255,
> -11.045, 6.33, -1.46, 33.385, -26.69, 9, 29.405, -29.125, 6.57,
> 34.56, -4.67, -17.94, 28.615, -28.205, 10.95, -2.545, 30.49,
> 26.935, -4.45, -7.855, -14.835, 29.88, 7.95, 34.84, 39.8, -28.745,
> 38.275, 43.15, -19.85, 10.695, 0.43, -0.78, -5.69, -5.285, 38.085,
> 0.685, -3.385, -2.515, 15.44, -20.16, 40.185, 50.705, -6.71,
> -37.8, 28.555, -1.58, -0.065, -10.97, 36.505, 48.14, -19.835,
> -5.755, 18.3, 14.4, 7.28, 6.965, 36.95, 24.62, -29.885, 16.33,
> 10.795, -12.5, -0.58, -7.085, 14.885, -14.515, 0.53, 5.84, -32.88,
> 29.945, -13.44, 23.045, 65.91, 31.525, 20.04, 17.94, -7.855,
> -27.86, -8.355, 15.41, 18.165, 18.425, 47.655, 51.59, 56.745,
> -2.39, -42.475, 18.05, -14.01, 23.055, -42.19, -24.14, 26.935,
> 66.305, 68.565, 71.13, 74.72, 38.305, -6.09, -14.18, 31.73, 5.025,
> -4.035, -22.18, -16.525, -15.675, 37.645, 23.95, 36.48, -12.39,
> 47.24, 48.425, -37.45, 18.13, 6.78, 22.71, -40.75, -17.15, 30.16,
> 41.445, -1.52, 8.795, -2.91, 27.955, 22.075, -12.75, -19.575,
> -20.53, 12.665, -7.415, -12.54, 16.46, 23.89, 41.805, -13.615,
> -1.475, 38.37, 33.15, 46.965, 33.04, 18.575, -6.08, 10.935, 19.14,
> 17.165, 38.645, 40.49, 25.725, 25.785, 16.285, 46.095, 8.95,
> 15.15, -18.045, 45.095, 26.115, 37.54, -0.295, -2.77, -3.445,
> 46.19, -10.32, 11.33, -6.09, -5.435, 17.76, -26.505, -24.855,
> -2.89, 31.965, 42.825, -19.13, 30.43, 29.525, -13.855, 22.8,
> 0.29, 33.635, 19.055, 37.14, 4.755, -5.4, -1.7, 26.87, -7.1,
> 19.81, 33.005, 15.805, 1.15, 42.47, 10.73, -15.695, 32.38, 27.93,
> 45.155, -26.425, -21.545, 36.165, -21.265, 5.775, 20.55, -0.885,
> 2.82, 8.16, -7.37, 19.11, 39.72, 40.5, -7.91, 19.43, 23.605,
> 16.935, -11.65, 8.99, 9, 18.845, 41.575, 33.51, -29.935, 37.055,
> -28.54, -31.89, 18.34, -32.745, -15.29, -0.96, 0.41, 3.235, 4.12,
> 12.505, 22.675, 26.05, 35.625, 38.825, 39.015, 40.825, 42.075,
> 43.48, 44.33, 46.735, 53.115, 57.18, 60.945, 42.555, 21.825,
> 30.85, 37.205, -26, -28.705, -25.1, 13.195, 22.515, 17.925, -24.31,
> -3.495, 3.08, 20.91, -34.72, 18.98, 22.035, 41.88, -1.83, 7.37,
> 17.175, 39.735, -21.705, 4.835, -28.215, -21.96, 29.755, -5.74,
> 32.945, 35.14, 21.065, 20.885, -19.72, -5.18, 8.745, 36.335,
> 17.01, 46.885, 16.285, 27.935, -36.145, -0.85, 12.935, 18.34,
> 26.99, 26.335, 14.32, 32.01, 5.675, -25.82, -32.665, 4.035, 14.055,
> 16.65, 20.585, 30.365, 38.725, 46.025, -42.595, 81.835, -32.405,
> 24.455, 12.87, 30.595, 20.505, -29.405, 19.99, 42.565, 6.78,
> 12.84, 39.43, 20.065, 35.13, 35.91, 18.39, -34.33, -5.805, 20.715,
> 18.18, 19.575, 20.535, 44.73, 42.605, -13.615, 7.745, 11.37,
> 9.455, 42.595, 31.305, 9.835)
>
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