Interpretation of insignificant interaction terms

[Emin Gurbanov]

I have two predictors in ordered logit model. A( income scale coded as 1- 10) and B (religious individual 1- yes, 0-no)
Dummies for income and for religious are significant, but interaction terms are not.
How to interpret and handle this situation? Should I retain the interaction term in the equation? Does it mean that B is insignificant after all?
Thanks a lot

[Marcos Almeida]

The best way to approach your query would be presenting command and output, as recommended in the FAQ.

That said, without a significant p-value for the interaction term, your model wouldn't "improve" much by maintaing it.

But you shouldn't take is as bad news. In fact, generally speaking, that means both predictors are important to your model, and you shouldn't be concerned about interaction between both.

[Emin Gurbanov]

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(happiness internal) byte(income education) float d byte male float GNIcap int age float age2 byte(nchildren empl) float refincome byte marital float health int year
3 0  5  8  6 0 2 43 1849  2 1 5.60199 1 5 1998
4 0  6  6  9 0 2 24  576  1 1 5.60199 1 2 2002
3 1  6  8  9 0 2 32 1024  1 1 5.60199 1 4 1998
3 0  4  6  9 0 2 52 2704  3 1 5.60199 1 4 2002
3 1  6  4  9 0 2 42 1764  1 1 5.60199 1 4 2002
3 1  7  5  9 0 2 38 1444  3 1 5.60199 1 4 2002
2 0  5  7  0 0 2 33 1089  2 1 5.60199 1 5 2002
3 0  4  4  8 0 2 51 2601  2 1 5.60199 1 5 2002
3 0  7  4  7 0 2 41 1681  2 1 5.60199 1 5 1998
3 1  4  4  9 0 2 47 2209  4 1 5.60199 1 4 2002
3 . .a  5  7 0 2 58 3364 .a 1 5.60199 1 4 2008
3 0  4  4  0 0 2 34 1156  3 1 5.60199 1 4 2002
3 0  6  8  6 0 2 24  576  0 1 5.60199 0 5 1998
2 1  7  4  5 0 2 32 1024  2 1 5.60199 1 5 2002
3 0  6  1  7 0 2 19  361  0 1 5.60199 0 4 1998
2 0  5  4  6 0 2 42 1764  2 1 5.60199 1 4 1998
2 0  4  4  6 0 2 24  576  0 1 5.60199 0 4 1998
2 0  5  6  6 0 2 35 1225  1 1 5.60199 1 3 1998
2 .  5  2  6 0 2 24  576  0 1 5.60199 0 5 1998
4 0  2  1  9 0 2 49 2401  2 1 5.60199 0 4 2002
2 . .a  7  6 0 2 45 2025 .a 1 5.60199 1 3 2008
3 1  7  8  9 0 2 26  676  0 1 5.60199 0 5 2002
3 1  8  6  8 0 2 45 2025  2 1 5.60199 1 5 2002
3 . .a  3  6 0 2 33 1089 .a 1 5.60199 1 5 2008
4 1  9  8  9 0 2 41 1681  2 1 5.60199 1 4 2002
2 1  4  1  9 0 2 32 1024  2 1 5.60199 1 4 2002
4 . .a  6  6 0 2 58 3364 .a 1 5.60199 1 3 2008
4 0  7  4  9 0 2 33 1089  2 1 5.60199 1 5 2002
3 0  8  5  8 0 2 37 1369  3 1 5.60199 1 5 2002
3 1  6  6  9 0 2 29  841  2 1 5.60199 1 5 2002
3 0  6  3  0 0 2 47 2209  3 1 5.60199 1 4 2002
3 0  4  2  6 0 2 23  529  0 1 5.60199 0 5 1998
3 . .a  7  6 0 2 54 2916 .a 1 5.60199 1 4 2008
2 0  4  8  6 0 2 34 1156  1 1 5.60199 1 4 1998
4 1  9  8  5 0 2 37 1369  2 1 5.60199 1 5 2002
2 . .a  6  6 0 2 54 2916 .a 1 5.60199 1 4 2008
4 . .a  7  6 0 2 30  900 .a 1 5.60199 1 4 2008
3 1  8  6  8 0 2 50 2500  2 1 5.60199 1 4 2002
3 1  4  8  9 0 2 42 1764  3 1 5.60199 1 3 2002
3 . .a  7  6 0 2 47 2209 .a 1 5.60199 1 4 2008
3 0  7  4  0 0 2 40 1600  1 1 5.60199 1 5 2002
3 0  9  7  9 0 2 33 1089  2 1 5.60199 1 5 2002
2 1  8  6  9 0 2 41 1681  2 1 5.60199 1 4 2002
2 1  4  4  7 0 2 45 2025  3 1 5.60199 1 4 1998
4 . .a  3  6 0 2 53 2809 .a 1 5.60199 1 4 2008
4 . .a  2  6 0 2 38 1444 .a 1 5.60199 1 3 2008
3 0  6  8  6 0 2 22  484  0 1 5.60199 0 4 1998
1 0  3  2  9 0 2 27  729  1 1 5.60199 1 4 2002
1 0  4  2  9 0 2 23  529  0 1 5.60199 0 3 2002
3 . .a  3  6 0 2 20  400 .a 1 5.60199 0 5 2008
2 0  3  8  0 0 2 45 2025  0 1 5.60199 0 4 2002
4 . .a .a  6 0 2 24  576 .a 1 5.60199 1 4 2008
3 . .a  7 .a 0 2 47 2209 .a 1 5.60199 0 4 2008
2 1  5  8  8 0 2 51 2601  2 1 5.60199 1 4 2002
2 1  5  2  9 0 2 24  576  0 1 5.60199 0 4 2002
2 .  2  4  6 0 2 24  576  0 1 5.60199 0 5 1998
2 1  5  8  8 0 2 37 1369  2 1 5.60199 1 4 2002
2 0  3  2  9 0 2 22  484  0 1 5.60199 0 4 1998
3 0  5  8  8 0 2 26  676  0 1 5.60199 0 4 2002
3 0  5  8  6 0 2 37 1369  3 1 5.60199 1 5 1998
2 1  .  8  7 0 2 23  529  0 1 5.60199 1 5 1998
3 . .a  6  6 0 2 51 2601 .a 1 5.60199 1 4 2008
2 0  4  4  6 0 2 40 1600  1 1 5.60199 1 4 1998
3 . .a  4  6 0 2 38 1444 .a 1 5.60199 1 4 2008
4 . .a  7 .a 0 2 28  784 .a 1 5.60199 1 4 2008
3 0  6  8  9 0 2 34 1156  2 1 5.60199 1 5 2002
3 0  8  8  6 0 2 24  576  0 1 5.60199 0 5 1998
3 0  5  7  9 0 2 24  576  1 1 5.60199 1 4 2002
3 . .a  3  6 0 2 21  441 .a 1 5.60199 0 5 2008
3 0  5  4  9 0 2 55 3025  4 1 5.60199 1 5 2002
3 1 10  4  8 0 2 34 1156  2 1 5.60199 1 4 2002
3 1  6  6  8 0 2 33 1089  2 1 5.60199 1 4 2002
3 0  7  4  8 0 2 47 2209  2 1 5.60199 1 5 2002
3 . .a  3  6 0 2 26  676 .a 1 5.60199 1 4 2008
3 . .a  5 .a 0 2 45 2025 .a 1 5.60199 0 3 2008
3 . .a  2  6 0 2 45 2025 .a 1 5.60199 1 3 2008
3 1  3  2  5 0 2 55 3025  4 1 5.60199 1 4 2002
3 . .a  7  6 0 2 47 2209 .a 1 5.60199 0 4 2008
3 . .a  7 .a 0 2 23  529 .a 1 5.60199 1 3 2008
2 . .a  7  7 0 2 44 1936 .a 1 5.60199 1 3 2008
2 1  3  6  8 0 2 24  576  1 1 5.60199 1 5 2002
2 0  3  2  6 0 2 35 1225  0 1 5.60199 1 3 1998
2 . .a  5 .a 0 2 73 5329 .a 1 5.60199 0 2 2008
3 . .a  7 .a 0 2 33 1089 .a 1 5.60199 1 3 2008
2 . .a  7  6 0 2 25  625 .a 1 5.60199 0 3 2008
3 1  6  8  7 0 2 24  576  0 1 5.60199 1 4 1998
3 . .a  3 .a 0 2 40 1600 .a 1 5.60199 1 5 2008
2 0  3  4  6 0 2 47 2209  4 1 5.60199 1 5 1998
3 . .a  6  6 0 2 23  529 .a 1 5.60199 0 3 2008
2 . .a  6  6 0 2 35 1225 .a 1 5.60199 1 4 2008
3 0  6  8  6 0 2 23  529  0 1 5.60199 0 5 1998
3 . .a  2 .a 0 2 33 1089 .a 1 5.60199 1 5 2008
2 1  3  4  8 0 2 56 3136  3 1 5.60199 1 3 2002
2 1  6  2  9 0 2 36 1296  2 1 5.60199 1 5 2002
3 . .a  7  6 0 2 52 2704 .a 1 5.60199 1 4 2008
4 . .a  5 .a 0 2 30  900 .a 1 5.60199 1 3 2008
3 0  7  3  0 0 2 39 1521  5 1 5.60199 1 5 2002
1 . .a  8  7 0 2 63 3969 .a 1 5.60199 1 4 2008
2 . .a  5 .a 0 2 53 2809 .a 1 5.60199 1 4 2008
3 . .a  6 .a 0 2 46 2116 .a 1 5.60199 1 3 2008
end
label values income X047
label def X047 2 "second step", modify
label def X047 3 "Third step", modify
label def X047 4 "Fourth step", modify
label def X047 5 "Fifth step", modify
label def X047 6 "Sixth step", modify
label def X047 7 "Seventh step", modify
label def X047 8 "Eigth step", modify
label def X047 9 "Nineth step", modify
label def X047 10 "Tenth step", modify
label values education X025
label def X025 1 "Inadequately completed elementary education", modify
label def X025 2 "Completed (compulsory) elementary education", modify
label def X025 3 "Incomplete secondary school: technical/vocational type", modify
label def X025 4 "Complete secondary school: technical/vocational type/secondary", modify
label def X025 5 "Incomplete secondary: university-preparatory type/Secondary,", modify
label def X025 6 "Complete secondary: university-preparatory type/full secondary", modify
label def X025 7 "Some university without degree/higher education - lower-level tertiary", modify
label def X025 8 "University with degree/higher education - upper-level tertiary", modify
label values male X001
label values age X003
label values nchildren X011
label def X011 0 "No child", modify
label def X011 1 "1 child", modify
label def X011 2 "2 children", modify
label def X011 3 "3 children", modify
label def X011 4 "4 children", modify
label def X011 5 "5 children", modify
label values empl X028
label def X028 1 "Full time", modify
label values marital X007
label def X007 1 "Married", modify
label values year S020
label def S020 1998 "1998", modify
label def S020 2002 "2002", modify
label def S020 2008 "2008", modify

[Emin Gurbanov]

--------------------------------------------------------------------
(1) (2) (3)
happiness happiness happiness
--------------------------------------------------------------------
happiness
internal=1 0.232*** 0.255*** 0.227***
(0.010) (0.032) (0.012)

second step 0.032 0.009
(0.019) (0.036)

Third step 0.061** 0.079*
(0.019) (0.034)

Fourth step 0.204*** 0.232***
(0.019) (0.033)

Fifth step 0.290*** 0.327***
(0.018) (0.032)

Sixth step 0.368*** 0.399***
(0.019) (0.034)

Seventh step 0.453*** 0.468***
(0.021) (0.036)

Eigth step 0.569*** 0.568***
(0.023) (0.040)

Nineth step 0.606*** 0.594***
(0.029) (0.048)

Tenth step 0.729*** 0.728***
(0.031) (0.049)

Inadequately compl~r 0.000 0.000 0.000
(.) (.) (.)

Completed (compuls~r 0.122*** 0.123*** 0.132***
(0.019) (0.019) (0.019)

Incomplete seconda~c 0.123*** 0.124*** 0.142***
(0.022) (0.022) (0.022)

Complete secondary~n 0.163*** 0.163*** 0.193***
(0.019) (0.019) (0.019)

Incomplete seconda~y 0.164*** 0.165*** 0.189***
(0.022) (0.022) (0.022)

Complete secondary~p 0.153*** 0.154*** 0.189***
(0.019) (0.020) (0.019)

Some university wi~h 0.153*** 0.154*** 0.197***
(0.023) (0.023) (0.023)

University with de~d 0.180*** 0.181*** 0.238***
(0.020) (0.020) (0.020)

Male -0.097*** -0.096*** -0.097***
(0.009) (0.009) (0.009)

GNIcap=1 0.000 0.000 0.000
(.) (.) (.)

GNIcap=2 -0.052*** -0.053*** -0.058***
(0.012) (0.012) (0.012)

GNIcap=3 0.011 0.010 0.002
(0.014) (0.014) (0.014)

Age -0.040*** -0.040*** -0.040***
(0.002) (0.002) (0.002)

age2 0.000*** 0.000*** 0.000***
(0.000) (0.000) (0.000)

1 child -0.026 -0.026 -0.032*
(0.015) (0.015) (0.015)

2 children 0.022 0.022 0.020
(0.015) (0.015) (0.015)

3 children 0.101*** 0.101*** 0.094***
(0.017) (0.017) (0.017)

4 children 0.096*** 0.096*** 0.084***
(0.021) (0.021) (0.021)

5 children 0.121*** 0.121*** 0.110***
(0.027) (0.027) (0.027)

6 children 0.164*** 0.163*** 0.149***
(0.034) (0.034) (0.034)

7 children 0.214*** 0.214*** 0.196***
(0.046) (0.046) (0.046)

8 or more children 0.279*** 0.279*** 0.263***
(0.038) (0.038) (0.038)

Part time 0.061*** 0.061*** 0.061***
(0.017) (0.017) (0.017)

Self employed 0.070*** 0.070*** 0.077***
(0.015) (0.015) (0.015)

Retired 0.051* 0.051* 0.061**
(0.020) (0.020) (0.020)

Housewife 0.194*** 0.194*** 0.202***
(0.016) (0.016) (0.016)

Students 0.089*** 0.089*** 0.085***
(0.020) (0.020) (0.019)

Unemployed -0.249*** -0.248*** -0.245***
(0.017) (0.017) (0.017)

Other 0.127*** 0.126*** 0.137***
(0.032) (0.032) (0.032)

refincome 0.022*** 0.022*** 0.049***
(0.006) (0.006) (0.006)

Married 0.372*** 0.372*** 0.389***
(0.011) (0.011) (0.011)

health=2 0.830*** 0.831*** 0.837***
(0.069) (0.069) (0.069)

health=3 1.749*** 1.750*** 1.769***
(0.067) (0.067) (0.067)

health=4 2.424*** 2.425*** 2.453***
(0.067) (0.067) (0.067)

health=5 3.504*** 3.505*** 3.537***
(0.068) (0.068) (0.068)

internal=0 # Lower~p 0.000
(.)

internal=0 # secon~p 0.000
(.)

internal=0 # Third~p 0.000
(.)

internal=0 # Fourt~p 0.000
(.)

internal=0 # Fifth~p 0.000
(.)

internal=0 # Sixth~p 0.000
(.)

internal=0 # Seven~p 0.000
(.)

internal=0 # Eigth~p 0.000
(.)

internal=0 # Ninet~p 0.000
(.)

internal=0 # Tenth~p 0.000
(.)

internal=1 # Lower~p 0.000
(.)

internal=1 # secon~p 0.033
(0.043)

internal=1 # Third~p -0.026
(0.040)

internal=1 # Fourt~p -0.041
(0.040)

internal=1 # Fifth~p -0.054
(0.038)

internal=1 # Sixth~p -0.045
(0.040)

internal=1 # Seven~p -0.020
(0.042)

internal=1 # Eigth~p 0.005
(0.047)

internal=1 # Ninet~p 0.021
(0.058)

internal=1 # Tenth~p 0.007
(0.061)

d_income=0 0.000
(.)

d_income=1 0.299***
(0.015)

internal=0 # d_inc~0 0.000
(.)

internal=0 # d_inc~1 0.000
(.)

internal=1 # d_inc~0 0.000
(.)

internal=1 # d_inc~1 0.009
(0.018)
--------------------------------------------------------------------
Observations 221973 221973 221973
Pseudo R-squared 0.104 0.104 0.103
AIC 434084.989 434093.157 434731.328
BIC 434920.125 435021.085 435494.291
--------------------------------------------------------------------
Standard errors in parentheses
* p<0.05, ** p<0.01, *** p<0.001

[Emin Gurbanov]

stata code is as follows:


ologit happiness i.internal i.income i.education i.d i.male i.GNIcap age age2 i.nchildren i.empl refincome i.marital i.health i.year, nolog
est store c1

ologit happiness i.internal##i.income i.education i.d i.male i.GNIcap age age2 i.nchildren i.empl refincome i.marital i.health i.year, nolog
est store c2


gen d_income=income
replace d_income=0 if income==1 | income==2 | income==3 | income==4 | income==5
replace d_income=1 if income==6 | income==7 | income==8 | income==9 | income==10


ologit happiness i.internal##i.d_income i.education i.d i.male i.GNIcap age age2 i.nchildren i.empl refincome i.marital i.health i.year, nolog
est store c3





esttab c1 c2 c3 using "out\Table7.doc", se(%9.3f) ///
b(%9.3f) pr2(%9.3f) aic(%12.3f) bic(%12.3f) ///
drop(*.year *.d _cons 0.internal 1.income 0.male 0.d 1.empl 0.marital 0.nchildren 1.health) label replace

[Marcos Almeida]

As underlined in #2, the second command did not seem to improve the model. Neither the third as well.

For the moment, I have just a smartphone and cannot test the command in Stata.