Random Coefficient Model

[Shisho Jakas]

Hi statalists,

I need your help.
I am currently trying to estimate the model (3) by plugging (2) into (1)
(1) yi = b₀ + b_{1i *} x_i + b_{2i *} z_i + e_i
(2) b_1i = g₀ + g_{1 *} pi + g_{2 *} z_i + u_i

(3) yi = b₀ + (g₀ + g_{1 *} pi + g_{2 *} z_i + u_i)_* x_i + b_{2i *} z_i + e_i
= b₀ + g_0*x_i + g_1*p_i*x_ii + g_2*z_i*x_i+ u_i*x_i + b_2i* z_i + e_i

This is the random coefficient model.
What kind of command I have to use to estimate?

For xi, I have edu( years of schooling ) and for zi, I have age, age (age squared), and urban.
For pi, I have pre (precipitaion)

Thank you in advance.

[Maarten Buis]

help mixed

[Shisho Jakas]

Thank you Maarten for replying!
I looked up the helped mixed and I am still confusing.
I think that I do not get the concept about the variables.
Could you give me a hint on my code based on the model and variable I have?

So in my case, what is the level variable?

I tried
Code:
mixed ttlwages || edu age age_squ urban:

but it did not go well. It says level edu age age_squ urban incorrectly specified


and plus,
after estimating this model, where or how can I find the distribution estimated?
Here is my data from dataex

* Example generated by -dataex-. To install: ssc install dataex
clear
input long(persid ttlwages) float edu byte age float age_squ byte urban double preci
 10150302     0  4 35 1225 1 70.3422
 30790104     0  4 32 1024 0 5.87504
 10150301     0  . 36 1296 1 70.3422
 40140102     0  . 40 1600 0 121.639
 80670701     0  5 49 2401 0 5.87504
 40140101     0  6 41 1681 0 121.639
 10240702  9000  . 29  841 0 12.6427
 10241002 10000  . 49 2401 0 12.6427
 10240402 12000  . 39 1521 0 12.6427
 40240902 14000  6 32 1024 0 27.8573
220040502 14000  9 26  676 1 70.3422
150161201 15000  6 73 5329 0 5.87504
 20641002 15000  5 25  625 0 213.632
170240201 15000  . 42 1764 0 12.6427
 30390202 18000  7 19  361 0 27.8573
121510201 20000  8 71 5041 1 70.3422
 30080402 20000  5 37 1369 1 5.87504
 70081001 20000 12 24  576 0 341.446
 20260902 20000  8 28  784 0 293.869
 20260901 20000  8 30  900 0 293.869
200180201 20000  7 32 1024 0 341.446
121320901 20000  7 76 5776 1 293.869
 20370802 23000  . 19  361 0 12.6427
 10050705 25000 18 21  441 1 121.639
 10230102 25000  4 33 1089 0 12.6427
170411201 25300  3 40 1600 0 5.87504
160031102 30000  6 59 3481 1 5.87504
 10240302 30000  . 54 2916 0 12.6427
 10310802 30000  . 66 4356 0 5.87504
 31060303 30000  . 70 4900 0 5.87504
 30980903 30000  7 27  729 0 341.446
 10261203 30000  8 18  324 0 334.451
150101101 30000  5 46 2116 0 334.451
210401201 30000  7 52 2704 0 102.575
 10311102 30000  . 48 2304 0 5.87504
 90100902 30000  4 22  484 0 27.8573
 80440202 30000  4 31  961 0 5.87504
 50530102 30000  2 55 3025 0 5.87504
210010902 30000  2 31  961 1 315.577
 80511101 30000  4 63 3969 0 27.8573
150201101 30000  5 60 3600 0 334.451
 31060206 30000  4 51 2601 0 5.87504
 30370101 30000  7 42 1764 0 293.869
 20010801 30000  . 33 1089 1 70.3422
220100401 35000  8 40 1600 0 121.639
 30321004 37500  3 23  529 0 5.87504
 30321001 37500  4 53 2809 0 5.87504
 30921101 37500  . 48 2304 0 85.5155
 30321003 37500  6 25  625 0 5.87504
 30881102 40000  5 24  576 0 27.8573
 10241102 40000  . 40 1600 0 12.6427
 10260101 40000  3 37 1369 0 334.451
 40050503 40000  7 30  900 1 85.5155
121030501 40000  8 69 4761 1 5.87504
 10240202 40000  . 46 2116 0 12.6427
100170501 40000  6 45 2025 0 12.6427
 10240501 40000  8 26  676 0 12.6427
 50191001 40000  3 44 1936 0 213.632
 40150806 40000  8 18  324 0 121.639
 10030701 40000  8 55 3025 1 315.577
140480703 40000 13 32 1024 0 12.6427
140221201 40000  . 51 2601 0 213.632
 30881002 40000  . 58 3364 0 27.8573
140221201 40000  . 51 2601 0 213.632
100131203 40000 10 37 1369 0 213.632
240220901 40000  4 55 3025 1 341.446
 30250903 40000  8 24  576 0 334.451
 30250904 40000 13 32 1024 0 334.451
 50601101 40000 13 27  729 0 293.869
 90101102 40000  7 27  729 0 27.8573
 31060501 40000  5 53 2809 0 5.87504
 40050501 40000  9 58 3364 1 85.5155
 50580503 40000  . 29  841 0 341.446
130080101 40000  6 24  576 0 341.446
150201204 42000 10 23  529 0 334.451
 30340501 42500  5 29  841 0 70.3422
200081003 44000 11 25  625 0 85.5155
 10241202 45000  2 49 2401 0 12.6427
 30370304 45000  7 22  484 0 293.869
 10241201 45000  . 49 2401 0 12.6427
 30380602 45000  . 50 2500 0 293.869
 20231203 45000 15 21  441 0 293.869
 30380601 45000  . 45 2025 0 293.869
 10241101 45000  . 30  900 0 12.6427
 10260102 46000  . 44 1936 0 334.451
140331201 48000  5 25  625 0 70.3422
 30021104 48000  8 27  729 1 334.451
121661004 48000  7 24  576 0 12.6427
 30610903 48000  0 30  900 0 293.869
 30450403 48000  9 27  729 0 213.632
 80571204 48000 10 31  961 0 315.577
 80571203 48000  4 34 1156 0 315.577
 50700401 48000  6 30  900 0 12.6427
 80370903 48000 10 44 1936 0 334.451
200131104 48000  . 21  441 0 12.6427
120281005 50000 13 31  961 1 121.639
170230703 50000  4 20  400 0 12.6427
121670401 50000  5 59 3481 0 12.6427
220041202 50000  . 49 2401 1 70.3422
160190201 50000  2 50 2500 0 5.87504
end

[Shisho Jakas]

Can anyone help?

[Carlo Lazzaro]

Shisho:
you should read (at least) -mixed- entry carefully again (examples on pigs growth are really interesting) before trying to sketch any mixed model code: they're really demanding to conceive, decipher and disseminate.
You might also be interested in the very well written and (pretty) easy to grasp: http://uk.sagepub.com/en-gb/eur/mult...age/book235963.
That said:
1) it is not clear from your code if you're actualy interested in a random intercept or in a random coefficient mixed model. If the latter were the case, please note that you have to select the variable that allows for a random slope;
2) why creating -age-squ- by hand when -fvvarlist- can create that for you?
3) your model(s) are not expected to converge (that is, you should revise your dataset and/or your model specification), as you can see form the following example:

*Random intercept model*
. mixed ttlwages c.age##c.age urban edu || persid:

Performing EM optimization:

Performing gradient-based optimization:

could not calculate numerical derivatives -- discontinuous region with missing values encountered
could not calculate numerical derivatives -- discontinuous region with missing values encountered
r(430);

*Random coefficient model (also known as (aka): random slope model); random slope on urban*

. mixed ttlwages c.age##c.age edu || persid: urban

Performing EM optimization:

Performing gradient-based optimization:

Iteration 0:   log likelihood = -804.60138  (not concave)
Iteration 1:   log likelihood = -804.38868  (not concave)
Iteration 2:   log likelihood = -804.31495  (not concave)
Iteration 3:   log likelihood = -804.30858  (not concave)
Iteration 4:   log likelihood = -804.30857  (not concave)
Iteration 5:   log likelihood = -804.30857  (not concave)
Iteration 6:   log likelihood = -804.30857  (not concave)
Iteration 7:   log likelihood = -804.30857  (not concave)
Iteration 8:   log likelihood = -804.30857  (not concave)
Iteration 9:   log likelihood = -804.30857  (not concave)
Iteration 10:  log likelihood = -804.30857  (not concave)
Iteration 11:  log likelihood = -804.30857  (not concave)
Iteration 12:  log likelihood = -804.30857  (not concave)
Iteration 13:  log likelihood = -804.30857  (not concave)
Iteration 14:  log likelihood = -804.30857  (not concave)
Iteration 15:  log likelihood = -804.30857  (not concave)
Iteration 16:  log likelihood = -804.30857  (not concave)
Iteration 17:  log likelihood = -804.30857  (not concave)
Iteration 18:  log likelihood = -804.30857  (not concave)
Iteration 19:  log likelihood = -804.30857  (not concave)
Iteration 20:  log likelihood = -804.30857  (not concave)
Iteration 21:  log likelihood = -804.30857  (not concave)
Iteration 22:  log likelihood = -804.30857  (not concave)
Iteration 23:  log likelihood = -804.30857  (not concave)
Iteration 24:  log likelihood = -804.30857  (not concave)
Iteration 25:  log likelihood = -804.30857  (not concave)
Iteration 26:  log likelihood = -804.30857  (not concave)
Iteration 27:  log likelihood = -804.30857  (not concave)
Iteration 28:  log likelihood = -804.30857  (not concave)
Iteration 29:  log likelihood = -804.30857  (not concave)
Iteration 30:  log likelihood = -804.30857  (not concave)
Iteration 31:  log likelihood = -804.30857  (not concave)
--Break--
r(1);