constructing a multilevel regression with random effects

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antonet
antonet on 27 Sep 2012
Dear all,
I have
A={
type_of_loan rates country number_of observat number_of_loans number_of_brands num_of_regions
[ 50] [59.4676] [1] [ 1] [1] [1] [1]
[ 50] [60.5912] [1] [ 2] [2] [1] [1]
[ 50] [60.6639] [1] [ 3] [3] [1] [1]
[150] [18.0268] [1] [ 4] [1] [2] [1]
[ 40] [71.5121] [1] [ 5] [2] [2] [1]
[150] [18.0490] [1] [ 6] [3] [2] [1]
[150] [24.8137] [1] [ 7] [1] [3] [1]
[150] [14.4040] [1] [ 8] [2] [3] [1]
[150] [24.5367] [1] [ 9] [3] [3] [1]
[150] [13.7685] [1] [10] [1] [4] [1]
[150] [13.8424] [1] [11] [2] [4] [1]
[150] [43.5706] [1] [12] [3] [4] [1]
[ 50] [62.1655] [1] [13] [1] [1] [2]
[ 50] [62.5669] [1] [14] [2] [1] [2]
[ 50] [62.8517] [1] [15] [3] [1] [2]
[150] [16.8333] [1] [16] [1] [2] [2]
[ 40] [68.6505] [1] [17] [2] [2] [2]
[150] [16.7442] [1] [18] [3] [2] [2]
[150] [22.9361] [1] [19] [1] [3] [2]
[150] [13.4317] [1] [20] [2] [3] [2]
[150] [22.7204] [1] [21] [3] [3] [2]
[150] [13.3108] [1] [22] [1] [4] [2]
[150] [13.3286] [1] [23] [2] [4] [2]
[150] [41.3907] [1] [24] [3] [4] [2]
[ 50] [61.5225] [1] [25] [1] [1] [3]
[ 50] [62.3809] [1] [26] [2] [1] [3]
[ 50] [62.5472] [1] [27] [3] [1] [3]
[150] [18.3575] [1] [28] [1] [2] [3]
[ 40] [71.6378] [1] [29] [2] [2] [3]
[150] [18.2007] [1] [30] [3] [2] [3]
[150] [23.9379] [1] [31] [1] [3] [3]
[150] [13.4733] [1] [32] [2] [3] [3]
[150] [23.7831] [1] [33] [3] [3] [3]
[150] [13.6555] [1] [34] [1] [4] [3]
[150] [13.5768] [1] [35] [2] [4] [3]
[150] [41.7986] [1] [36] [3] [4] [3]
[ 50] [58.8043] [1] [37] [1] [1] [4]
[ 50] [59.8979] [1] [38] [2] [1] [4]
[ 50] [60.1406] [1] [39] [3] [1] [4]
[150] [19.4341] [1] [40] [1] [2] [4]
[ 40] [72.7402] [1] [41] [2] [2] [4]
[150] [18.5913] [1] [42] [3] [2] [4]
[150] [25.3780] [1] [43] [1] [3] [4]
[150] [14.3916] [1] [44] [2] [3] [4]
[150] [25.0602] [1] [45] [3] [3] [4]
[150] [13.9212] [1] [46] [1] [4] [4]
[150] [13.8527] [1] [47] [2] [4] [4]
[150] [44.4282] [1] [48] [3] [4] [4]
[ 50] [66.3466] [1] [49] [1] [1] [5]
[ 50] [69.3246] [1] [50] [2] [1] [5]
[ 50] [63.7933] [1] [51] [3] [1] [5]
[150] [19.4466] [1] [52] [1] [2] [5]
[ 40] [48.1944] [1] [53] [2] [2] [5]
[150] [18.6439] [1] [54] [3] [2] [5]
[150] [27.5151] [1] [55] [1] [3] [5]
[150] [13.6534] [1] [56] [2] [3] [5]
[150] [27.5469] [1] [57] [3] [3] [5]
[150] [15.8198] [1] [58] [1] [4] [5]
[150] [15.1235] [1] [59] [2] [4] [5]
[150] [49.0785] [1] [60] [3] [4] [5]
[ 50] [59.6975] [1] [61] [1] [1] [6]
[ 50] [60.4081] [1] [62] [2] [1] [6]
[ 50] [60.7452] [1] [63] [3] [1] [6]
[150] [19.5396] [1] [64] [1] [2] [6]
[ 40] [75.3618] [1] [65] [2] [2] [6]
[150] [18.5875] [1] [66] [3] [2] [6]
[150] [25.9974] [1] [67] [1] [3] [6]
[150] [14.7011] [1] [68] [2] [3] [6]
[150] [25.9541] [1] [69] [3] [3] [6]
[150] [13.9805] [1] [70] [1] [4] [6]
[150] [14.3128] [1] [71] [2] [4] [6]
[150] [44.9720] [1] [72] [3] [4] [6]
[ 50] [60.2959] [1] [73] [1] [1] [7]
[ 50] [60.8045] [1] [74] [2] [1] [7]
[ 50] [60.9119] [1] [75] [3] [1] [7]
[150] [19.1844] [1] [76] [1] [2] [7]
[ 40] [71.7604] [1] [77] [2] [2] [7]
[150] [19.0658] [1] [78] [3] [2] [7]
[150] [26.1284] [1] [79] [1] [3] [7]
[150] [15.2403] [1] [80] [2] [3] [7]
[150] [25.9214] [1] [81] [3] [3] [7]
[150] [13.5574] [1] [82] [1] [4] [7]
[150] [13.5555] [1] [83] [2] [4] [7]
[150] [40.9040] [1] [84] [3] [4] [7]}
Tha above matrix says that for country 1 (third column) we have totally 84 observations (column 4) on 2 variables; type of loans and interest rates (column 1 and 2 respectively). These rates are broken down by 7 regions (last column ) each of which has 4 brands (sixth column) and each brand offers 3 types of loans(fifth column) the numerical value of which is given in the first column.
The goal is to run the following multilevel regression with random effects
rates_{country}_{regions}_{brands}= a + b*type_of_loan_{country}_{regions}_{brands}+a_{regions}+c_{brands}+error_{country}_{regions}_{brands}
where the {country}_{regions}_{brands} is the index and a_{regions}+c_{brands} are random effects for regions and brands respectively.
So rates vary across countries, regions and brands and I have similar A matrices for the rest of the countries.
I am struggling to find a solution but so far I can't.
Any code provided will be greately appreciated.
thanks

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Answers (1)

Tom Lane
Tom Lane on 29 Sep 2012
Currently anovan is the only Statistics Toolbox function (aside from a couple aimed at nonlinear fitting) that supports random effects. It also supports nested factors. It seems like it might be appropriate here.
I can't say I fully understand your problem, though. Have you tried to set it up using anovan?

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