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st: constructing a multilevel regression model with fixed effects


From   sabbas gidarokostas <sabbasgidarokostas@googlemail.com>
To   statalist <statalist@hsphsun2.harvard.edu>
Subject   st: constructing a multilevel regression model with fixed effects
Date   Thu, 27 Sep 2012 17:10:37 +0200

A={
  type_of_poan  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
Sum(a_{regions})+sum(c_{brands}) are fixed 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.

I tried to apply a linear mixd model

 xtmixed   rates  type_of_loan ||   identif1_country: || storetype:
||brand:, mle difficult but I am not sure that this is the correct
way.

I also use stata 2011

Any code provided will be greately appreciated.

thanks in advance
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