Testing linearity with a plot of standardized residuals

[Gabriella Miniero]

Hi forum!
I have a question for you. I tried to assess the linearity assumption of my multiple linear regression model by testing the "structure" of the standardized residuals against the values of my predictors; but I'm not so sure this is the best way to do that. I attached an example of what I've done.

. regress consumilog disoccup inattivitàlog dem_impreselog retrib_medialog componenti_f
> amsqr

      Source |       SS       df       MS              Number of obs =     107
-------------+------------------------------           F(  5,   101) =  161.28
       Model |  5.44754193     5  1.08950839           Prob > F      =  0.0000
    Residual |  .682297905   101  .006755425           R-squared     =  0.8887
-------------+------------------------------           Adj R-squared =  0.8832
       Total |  6.12983984   106  .057828678           Root MSE      =  .08219

-----------------------------------------------------------------------------------
       consumilog |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
         disoccup |  -.0139411   .0028199    -4.94   0.000     -.019535   -.0083473
    inattivitàlog |  -.6843887   .0814612    -8.40   0.000    -.8459859   -.5227915
   dem_impreselog |    .015953   .0126544     1.26   0.210      -.00915     .041056
  retrib_medialog |   .3489728   .1838609     1.90   0.061    -.0157578    .7137034
componenti_famsqr |   .0385899   .0133636     2.89   0.005     .0120802    .0650997
            _cons |   6.341054   1.937408     3.27   0.001     2.497758    10.18435
-----------------------------------------------------------------------------------

predict consumires, rstandard

 scatter consumires disoccup

[Nick Cox]

Note that this plot is (almost) wired in as rvfplot -- and it is available through rvfplot2, as from

SJ-10-1 gr0009_1 . . . . Software update for model diagnostic graph commands
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. J. Cox
(help anovaplot, indexplot, modeldiag, ofrtplot, ovfplot,
qfrplot, racplot, rdplot, regplot, rhetplot, rvfplot2,
rvlrplot, rvpplot2 if installed)
Q1/10 SJ 10(1):164
provides new command rbinplot for plotting means or medians
of residuals by bins; provides new options for smoothing
using restricted cubic splines; updates anova examples

SJ-4-4 gr0009 . . . . . . . . . . Speaking Stata: Graphing model diagnostics
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. J. Cox
(help anovaplot, indexplot, modeldiag, ofrtplot, ovfplot,
qfrplot, racplot, rdplot, regplot, rhetplot, rvfplot2,
rvlrplot, rvpplot2 if installed)
Q4/04 SJ 4(4):449--475
plotting diagnostic information calculated from residuals
and fitted values from regression models with continuous
responses


Yes, it is a good idea, and we need to see yours to comment further.

Detail: the name rdplot was used by me in 2004 for a particular plot and later for other purposes for a different command in a very popular package. No-one that I know of has yet complained of the name clash, but watch out.

[Carlo Lazzaro]

Gabriella:
you can also give the issue an analytical try via -estat ovtest- and, probably more interesting, -linktest-.

[Gabriella Miniero]

and what about the the command acprplot (augmented component-plus-residual plot)?

[Carlo Lazzaro]

Gabriella:
personally, I find visual inspection more useful for detecting heteroskedasticity (which may well be a symptom of model misspecification).
When it comes to model misspecification (such as investigating the existence of squared relationship between predicto(s) and regressand), I prefer an analytical approach.

[Uyi Erhabor]

Hi everyone I hope you are all well,

I am trying to test the OLS regression assumption of no heteroskedasticity in Stata 16.1 before running this fixed effects regression model:

xtreg DiffMeanHourlyPercent Year2019 Year2020, fe

Which test would be appropriate for me to use given my independent variables are year dummies. I have not seen anything on the internet that specifically recommends a test to detect heteroskedasticity when there are only dummy independent variables present in a fixed effects regression model.

Kind regards,

Uyi Erhabor

(Stata 16.1 SE)

[Carlo Lazzaro]

Uyi:
some comments about your post:
- you should -reshape- your data in -long- format, so that you can have a -year- variable that becomes your -timevar-;
- under the -fe- specification, alle the time-invariant predictors will be wiped out;
- the visula inspection of the epsilon residual is recommended after (not before) -xtreg-, as no anlytical test is included among Stata built-in command.

[Uyi Erhabor]

Hi Carlo,

Thank you for your reply! Howcome the inspection should be carried out after the xtreg command?

Kind regards,

Uyi Erhabor

(Stata 16.1 SE)

[Uyi Erhabor]

Hi everyone,

Please could someone explain if this scatterplot exhibits heteroskedasticity? If so could you explain why.

Kind regards,

Uyi Erhabor

(Stata 16.1 SE)

[Carlo Lazzaro]

Uyi:

use "https://www.stata-press.com/data/r16/nlswork.dta"

. xtreg ln_wage i.nev_mar i.collgrad, fe
note: 1.collgrad omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =     28,518
Group variable: idcode                          Number of groups  =      4,711

R-sq:                                           Obs per group:
     within  = 0.0263                                         min =          1
     between = 0.0011                                         avg =        6.1
     overall = 0.0032                                         max =         15

                                                F(1,23806)        =     641.83
corr(u_i, Xb)  = -0.1414                        Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   1.nev_mar |  -.1929812   .0076174   -25.33   0.000    -.2079118   -.1780507
  1.collgrad |          0  (omitted)
       _cons |   1.719339   .0025617   671.17   0.000     1.714318    1.724361
-------------+----------------------------------------------------------------
     sigma_u |  .42825389
     sigma_e |   .3159974
         rho |  .64747634   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4710, 23806) = 8.76                 Prob > F = 0.0000

. predict e_res, e
(16 missing values generated)

. qnorm e_res

.