[Aye Aye Khaine]

Hello,
I did the U test. How shall I interpret? P value is insignificant. Does that mean that there is no shape? my model is linear without the squared term?



. utest agemo sq_age

Specification: f(x)=x^2
Extreme point: 42.57625

Test:
H1: U shape
vs. H0: Monotone or Inverse U shape

-------------------------------------------------
| Lower bound Upper bound
-----------------+-------------------------------
Interval | .00274 64.56667
Slope | -.0673668 .0347968
t-value | -15.02906 8.016549
P>|t| | 1.65e-50 6.40e-16
-------------------------------------------------

Overall test of presence of a U shape:
t-value = 8.02
P>|t| = 6.40e-16




Thanks so much

[Aye Aye Khaine]

Hi Clyde,
I am sorry. Please disregard my #12.
Warm regards,
Aye Aye Khaine

[Aye Aye Khaine]

Hello,

I did the margins plot on the regression model I presented earlier with the squared of age. My age ranges are from zero to sixty months. I got the following graph. I don't think it is actually U shaped. It is just a liner declining function as children ages and their height are not growing. Am I right? Is the graph below showing?

margins, at (agemo= (2 (4) 65))
marginsplot

[Clyde Schechter]

No graph is showing in #18.

[Aye Aye Khaine]

Hi,
How do I get the graph to show? I just did the simple cut and paste and it is not showing.

[Aye Aye Khaine]

Hello, here is the graph on the regression I posted with age and age squared. U shape test's p value was way above p>.10. so, not sure I need to do age squared??? please advise and hope to hear from you soon.
Best regards,
Aye Aye

[Clyde Schechter]

In #16 you show results of the -utest- command, and the pvalue is 6.40e-16. In ordinary scientific notation that's 6.4x10^-16. So why do you say p > .10? You know, I'm one of those people who doesn't like the concept of statistical significance at all, and am often dismissive of p-values, but even I would be loathe to go against a pvalue of 6.4x10^-16. Even though it is absurd to pretend that p-values have anything approaching that level of accuracy, you don't get a pvalue that small without something going on that's worth talking about.

Even ignoring p-values, the U-shapedness of the graph is unmistakeable. Even if the p-value really were > .10, I would call this a definitely U-shaped relationship.

[Aye Aye Khaine]

Hi Clyde,
Please let me try the following in the graph and please correct me if I am not making sense of the graph. the dependent variable was height for age z score (standard deviation)unit. Children <-2 z score are considered stunted.

The graph means that

at about 2 months of age, his or her height for age z score (or their height growth according to that age) is growing between .-5 (fish) and .-6 height for age z score. as a child reaches to 6 months old, their height for age z score between -8 and -9. Older children in my sample average height for age z score is low in general. However, all children are above -2 z score.


Is that how I should be making sense?

Thanks so much for your previous reply.

Hope to hear again soon. Please help and I got to get over this.

[Clyde Schechter]

You are reading the graph accurately, but you are misinterpreting its meaning. You cannot, from this graph, say anything about the height for age z-score of any one child, nor can you make statements such as "all children are above -2 z score." The predicted values that are plotted in that graph are the mean height-for-age z-scores at that age, adjusted for other variables in your model. So the average height for age is always above -2, but there may be many children whose height for age dips below that value. And you can't say anything about any single child from this graph. It is a graph of the average values (adjusted) only.

[Aye Aye Khaine]

Thank you so much, Professor Clyde!
Much appreciated!

[sophie maene]

Dear,

I estimated a random effects ordered probit model:

 xtoprobit shealth c.age##c.age i.wave, vce(cluster mergeid_n)

To see whether the turning point was included in my data i ran as was suggested in this thread.

nlcom -_b[age]/(2*_b[c.age#c.age])

The data in my sample runs from 65-95 but I receive

_nl_1:  -_b[age]/(2*_b[c.age#c.age])

------------------------------------------------------------------------------
     shealth |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   1427.445   5472.045     0.26   0.794    -9297.566    12152.46
------------------------------------------------------------------------------

The age 1427.445 simply does not exists. Any idea what is going on?

When I run:

 margins, at (age=(65(5)95)) nose
marginsplot

I get this margins plot:



Not sure of this margins plot proves that I should use age squared or not.

Thank you in advance!

[Carlo Lazzaro]

Sophie:
why not sharing -xtoprobit- outcome table, too? Thanks.

[sophie maene]

Hi, yes sorry here it is!

 xtoprobit shealth c.age##c.age i.wave, vce(cluster mergeid_n)

Fitting comparison model:

Iteration 0:   log likelihood = -220787.09  
Iteration 1:   log likelihood = -216727.71  
Iteration 2:   log likelihood = -216726.89  
Iteration 3:   log likelihood = -216726.89  

Refining starting values:

Grid node 0:   log likelihood = -209010.45

Fitting full model:

Iteration 0:   log pseudolikelihood = -209010.45  
Iteration 1:   log pseudolikelihood = -200663.47  
Iteration 2:   log pseudolikelihood =  -196345.3  
Iteration 3:   log pseudolikelihood = -195566.04  
Iteration 4:   log pseudolikelihood = -195532.62  
Iteration 5:   log pseudolikelihood = -195532.47  
Iteration 6:   log pseudolikelihood = -195532.47  

Random-effects ordered probit regression        Number of obs     =    154,711
Group variable: mergeid_n                       Number of groups  =     62,399

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          1
                                                              avg =        2.5
                                                              max =          7

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(8)      =    6777.25
Log pseudolikelihood  = -195532.47              Prob > chi2       =     0.0000

                         (Std. Err. adjusted for 62,399 clusters in mergeid_n)
------------------------------------------------------------------------------
             |               Robust
     shealth |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.0634849   .0137425    -4.62   0.000    -.0904197   -.0365502
             |
 c.age#c.age |   .0000222   .0000901     0.25   0.805    -.0001543    .0001987
             |
        wave |
          2  |  -.1946302    .014936   -13.03   0.000    -.2239043   -.1653562
          3  |  -.3675597   .0161868   -22.71   0.000    -.3992852   -.3358342
          4  |   -.243044   .0154814   -15.70   0.000     -.273387    -.212701
          5  |  -.1574564   .0153565   -10.25   0.000    -.1875545   -.1273583
          6  |  -.1856671   .0154187   -12.04   0.000    -.2158873    -.155447
          7  |  -.2027917   .0157322   -12.89   0.000    -.2336263   -.1719571
-------------+----------------------------------------------------------------
       /cut1 |  -6.501648   .5206987                     -7.522199   -5.481098
       /cut2 |  -4.913978   .5207371                     -5.934604   -3.893352
       /cut3 |  -3.246265   .5207259                     -4.266869   -2.225661
       /cut4 |  -2.076403   .5207411                     -3.097037    -1.05577
-------------+----------------------------------------------------------------
   /sigma2_u |   1.575051   .0200396                       1.53626    1.614822
------------------------------------------------------------------------------

[Carlo Lazzaro]

Sophie:
your results do not show evidence of a squared relationship for -age-.
That said, only the time dimension of your panel seems to play a role in explaining variations in the regressand.
That said, what strikes me is that you have -age- only as other predictors.
Are you sure that you gave a fair and true view of the data generating process?

[sophie maene]

I actually have a lot more variables in my model but thought that it would become a too long post so I just used the age squared: this is my full model

toprobit shealth c.age##c.age##i.LTCsystem female bmi i.co007_ eduyears_mod chronic_mod i.childhoodhealth eurod ever_smoked smoking i.br010_mod i.sportsoractivities ch001_ ch021_mod partnerinhh gdp i.wave, vce(cluster mergeid_n)

 xtoprobit shealth c.age##c.age##i.LTCsystem female bmi i.co007_ eduyears_mod chronic_mod i.childhoodhealth eurod ever_smoked smoking i
> .br010_mod i.sportsoractivities ch001_ ch021_mod partnerinhh gdp i.wave, vce(cluster mergeid_n)

Fitting comparison model:

Iteration 0:   log likelihood = -68026.187  
Iteration 1:   log likelihood =  -57366.91  
Iteration 2:   log likelihood = -57291.882  
Iteration 3:   log likelihood = -57291.846  
Iteration 4:   log likelihood = -57291.846  

Refining starting values:

Grid node 0:   log likelihood = -58448.777

Fitting full model:

Iteration 0:   log pseudolikelihood = -58448.777  (not concave)
Iteration 1:   log pseudolikelihood = -56606.722  
Iteration 2:   log pseudolikelihood =   -55660.1  
Iteration 3:   log pseudolikelihood = -55633.542  
Iteration 4:   log pseudolikelihood = -55633.321  
Iteration 5:   log pseudolikelihood = -55633.321  

Random-effects ordered probit regression        Number of obs     =     47,521
Group variable: mergeid_n                       Number of groups  =     26,564

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          1
                                                              avg =        1.8
                                                              max =          4

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(42)     =   11773.70
Log pseudolikelihood  = -55633.321              Prob > chi2       =     0.0000

                                            (Std. Err. adjusted for 26,564 clusters in mergeid_n)
-------------------------------------------------------------------------------------------------
                                |               Robust
                        shealth |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------------------+----------------------------------------------------------------
                            age |  -.0300641   .0482202    -0.62   0.533     -.124574    .0644458
                                |
                    c.age#c.age |   .0000321   .0003173     0.10   0.919    -.0005899    .0006541
                                |
                      LTCsystem |
                     Cluster 2  |   2.331213    2.42739     0.96   0.337    -2.426384    7.088811
                     Cluster 3  |   1.362363   2.425582     0.56   0.574     -3.39169    6.116417
                     Cluster 4  |   2.824523   2.755899     1.02   0.305    -2.576939    8.225986
                                |
                LTCsystem#c.age |
                     Cluster 2  |  -.0797573    .064341    -1.24   0.215    -.2058634    .0463488
                     Cluster 3  |  -.0385814   .0640747    -0.60   0.547    -.1641655    .0870027
                     Cluster 4  |  -.0881586   .0731019    -1.21   0.228    -.2314357    .0551185
                                |
          LTCsystem#c.age#c.age |
                     Cluster 2  |   .0005722   .0004242     1.35   0.177    -.0002592    .0014035
                     Cluster 3  |   .0002343   .0004209     0.56   0.578    -.0005906    .0010593
                     Cluster 4  |   .0006058   .0004824     1.26   0.209    -.0003397    .0015513
                                |
                         female |   .1099243   .0180642     6.09   0.000      .074519    .1453295
                            bmi |   -.028748   .0018042   -15.93   0.000    -.0322842   -.0252117
                                |
                         co007_ |
       2. With some difficulty  |   .1223905   .0272272     4.50   0.000     .0690263    .1757548
              3. Fairly easily  |   .2568748   .0284901     9.02   0.000     .2010352    .3127144
                     4. Easily  |   .3786829   .0299674    12.64   0.000     .3199479    .4374179
                                |
                   eduyears_mod |   .0350989   .0020617    17.02   0.000      .031058    .0391399
                    chronic_mod |  -.5988879   .0161005   -37.20   0.000    -.6304442   -.5673315
                                |
                childhoodhealth |
                        2.Poor  |  -.4891291   .1292088    -3.79   0.000    -.7423737   -.2358845
                        3.Fair  |  -.3603825   .1221198    -2.95   0.003    -.5997329    -.121032
                        4.Good  |  -.2329024   .1201075    -1.94   0.052    -.4683088     .002504
                   5.Very good  |  -.0536764   .1199848    -0.45   0.655    -.2888422    .1814895
                   6.Excellent  |   .1493303   .1202162     1.24   0.214    -.0862892    .3849499
                                |
                          eurod |  -.2254837   .0036085   -62.49   0.000    -.2325562   -.2184111
                    ever_smoked |  -.0774778    .018341    -4.22   0.000    -.1134255   -.0415302
                        smoking |  -.0065085   .0257136    -0.25   0.800    -.0569063    .0438893
                                |
                      br010_mod |
     2. less than once a month  |   .1802149   .0240414     7.50   0.000     .1330947    .2273352
      3. once or twice a month  |   .2578486   .0239887    10.75   0.000     .2108316    .3048655
       4. once or twice a week  |   .3625201   .0219147    16.54   0.000     .3195681    .4054721
  5. three or four days a week  |   .4214576    .029104    14.48   0.000     .3644148    .4785005
    6. five or six days a week  |   .4273772   .0399496    10.70   0.000     .3490775    .5056769
           7. almost every day  |   .3480736   .0209166    16.64   0.000     .3070778    .3890693
                                |
             sportsoractivities |
 2. One to three times a month  |   .4058166   .0225476    18.00   0.000     .3616241    .4500091
                3. Once a week  |    .451309   .0194354    23.22   0.000     .4132163    .4894018
       4.More than once a week  |   .5949294   .0168049    35.40   0.000     .5619923    .6278664
                                |
                         ch001_ |   .0028423   .0079224     0.36   0.720    -.0126853    .0183699
                      ch021_mod |   .0025406   .0031504     0.81   0.420     -.003634    .0087152
                    partnerinhh |  -.1024684   .0179812    -5.70   0.000    -.1377109    -.067226
                            gdp |   .0000116   1.24e-06     9.37   0.000     9.20e-06    .0000141
                                |
                           wave |
                             2  |  -.2832655   .0204394   -13.86   0.000     -.323326    -.243205
                             4  |  -.3138069   .0218063   -14.39   0.000    -.3565466   -.2710673
                             5  |  -.3327459   .0217811   -15.28   0.000    -.3754361   -.2900557
--------------------------------+----------------------------------------------------------------
                          /cut1 |  -5.117054   1.827863                       -8.6996   -1.534509
                          /cut2 |  -3.394676   1.828006                     -6.977502    .1881492
                          /cut3 |  -1.677042   1.827917                     -5.259693    1.905609
                          /cut4 |  -.5206001   1.827813                     -4.103048    3.061848
--------------------------------+----------------------------------------------------------------
                      /sigma2_u |   .7327147   .0234679                      .6881324    .7801854
-------------------------------------------------------------------------------------------------

Which gives the following marginsplot

 
  margins, at (age=(65(5)95)) nose marginsplot

So I guess no age square necessary!