clear all
use https://sscc.wisc.edu/sscc/pubs/real_world_tables/reg14 Multinomial Logit
Shifting now to tables of regression results, our first challenge is a multinomial regression model, where each outcome has its own set of coefficients. Our goal is to put them in separate columns. We also want relative risk ratios and confidence intervals, on one row, rather than coefficients and standard errors.
4.1 Setting Up
Load the data and take a moment to look it over and identify the variables.
4.2 Run the Model and Collect the Results
Run the regression model, including the rrr option to report relative risk ratios, and collect the results:
collect: mlogit involvement i.exposure i.race, rrr base(0)
Iteration 0: Log likelihood = -1373.9734
Iteration 1: Log likelihood = -1326.0187
Iteration 2: Log likelihood = -1325.2431
Iteration 3: Log likelihood = -1325.2429
Iteration 4: Log likelihood = -1325.2429
Multinomial logistic regression Number of obs = 1,000
LR chi2(15) = 97.46
Prob > chi2 = 0.0000
Log likelihood = -1325.2429 Pseudo R2 = 0.0355
------------------------------------------------------------------------------
involvement | RRR Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
None | (base outcome)
-------------+----------------------------------------------------------------
CPS_Only |
exposure |
CPS Only | 2.520022 .6523992 3.57 0.000 1.51719 4.185707
CLS Only | 1.563043 .4670294 1.49 0.135 .8702346 2.807409
Both CPS .. | 1.258737 .3508603 0.83 0.409 .7289055 2.173697
|
race |
Black | 1.173601 .2837658 0.66 0.508 .7306474 1.885094
Hispanic | .9474532 .221673 -0.23 0.818 .5989693 1.498687
|
_cons | .6896629 .1616981 -1.58 0.113 .4355765 1.091966
-------------+----------------------------------------------------------------
CLS_Only |
exposure |
CPS Only | .8276127 .2105479 -0.74 0.457 .5026645 1.362624
CLS Only | 2.539109 .6393221 3.70 0.000 1.550092 4.159157
Both CPS .. | .725354 .1884331 -1.24 0.216 .4359374 1.206913
|
race |
Black | 1.155772 .2583481 0.65 0.517 .7457687 1.791183
Hispanic | .6523108 .1456247 -1.91 0.056 .4211421 1.01037
|
_cons | 1.416345 .2906654 1.70 0.090 .9472914 2.117651
-------------+----------------------------------------------------------------
Both_CPS__~S |
exposure |
CPS Only | .9414855 .2508099 -0.23 0.821 .5585413 1.586982
CLS Only | 1.702195 .4650387 1.95 0.052 .9964641 2.90775
Both CPS .. | 1.685971 .4183011 2.11 0.035 1.036719 2.741821
|
race |
Black | 1.434602 .3397596 1.52 0.128 .9018611 2.282039
Hispanic | 1.218457 .2747452 0.88 0.381 .7832058 1.89559
|
_cons | .8273178 .1839026 -0.85 0.394 .5351317 1.27904
------------------------------------------------------------------------------
Note: _cons estimates baseline relative risk for each outcome.4.3 Structure the Table
To see what’s in the collection, run collect dims:
collect dims
Collection dimensions
Collection: default
-----------------------------------------
Dimension No. levels
-----------------------------------------
Layout, style, header, label
cmdset 1
coleq 4
colname 13
colname_remainder 1
exposure 4
program_class 1
race 3
result 48
result_type 3
rowname 1
Style only
border_block 4
cell_type 4
-----------------------------------------As usual, colname contains the predictors. It will be the rows of the table, but we’ll select only i.exposure and i.race.
collect levelsof colname
Collection: default
Dimension: colname
Levels: 0.exposure 1.exposure 2.exposure 3.exposure 0.race 1.race 2.race
c1 c2 c3 c4 _cons o._consresult contains the various available results from the model.
collect levelsof result
Collection: default
Dimension: result
Levels: N N_cd _r_b _r_ci _r_df _r_lb _r_p _r_se _r_ub _r_z _r_z_abs
baselab baseout chi2 chi2type cmd cmdline converged depvar
deriv_useminbound df_m eqnames ibaseout ic k k_dv k_eq k_eq_base
k_eq_model k_out ll ll_0 marginsdefault marginsnotok ml_method
opt out p predict properties r2_p rank rc technique title user
vce whichresult[_r_b] contains the coefficients as reported by the regression command, so in this case they are actually the relative risk ratios. result[_r_ci] contains the confidence intervals. We want the risk ratios and confidence intervals on the same row in two columns, so result[_r_b _r_ci] will be part of the column specification.
What about the four outcomes? They are found in coleq:
collect levelsof coleq
Collection: default
Dimension: coleq
Levels: None CPS_Only CLS_Only Both_CPS___CLSThe names of the levels are based on the value labels for the outcome variable, involvement. But they contain characters that can’t be used in collection levels, so collect had to adapt them.
The layout you need is:
collect layout (colname[i.exposure i.race]) (coleq[CPS_Only CLS_Only Both_CPS___CLS]#result[_r_b _r_ci])
Collection: default
Rows: colname[i.exposure i.race]
Columns: coleq[CPS_Only CLS_Only Both_CPS___CLS]#result[_r_b _r_ci]
Table 1: 7 x 6
----------------------------------------------------------------------------------------------------------------
| CPS_Only CPS_Only CLS_Only CLS_Only Both_CPS___CLS Both_CPS___CLS
| Coefficient 95% CI Coefficient 95% CI Coefficient 95% CI
---------------+------------------------------------------------------------------------------------------------
None | 1 1 1
CPS Only | 2.520022 1.51719 4.185707 .8276127 .5026645 1.362624 .9414855 .5585413 1.586982
CLS Only | 1.563043 .8702346 2.807409 2.539109 1.550092 4.159157 1.702195 .9964641 2.90775
Both CPS & CLS | 1.258737 .7289055 2.173697 .725354 .4359374 1.206913 1.685971 1.036719 2.741821
White | 1 1 1
Black | 1.173601 .7306474 1.885094 1.155772 .7457687 1.791183 1.434602 .9018611 2.282039
Hispanic | .9474532 .5989693 1.498687 .6523108 .4211421 1.01037 1.218457 .7832058 1.89559
----------------------------------------------------------------------------------------------------------------This omits the “model” for the base outcome (all ones) as well as specifying which results to include.
4.4 Clean Up
This is the structure we want, but the are a bunch of settings that need tweaking to give it a satisfactory appearance. Styles are collections of such settings, and can save you some work if you like what they do. Stata comes with some styles predefined, and you can create your own if you find yourself using the same settings repeatedly. In this case, the style table-reg1 will help with the columns headers, so apply it with collect style use:
collect style use table-reg1
collect preview
Collection: default
Rows: colname[i.exposure i.race]
Columns: coleq[CPS_Only CLS_Only Both_CPS___CLS]#result[_r_b _r_ci]
Table 1: 7 x 6
------------------------------------------------------------------------------------------------------------------------
| CPS_Only CLS_Only Both_CPS___CLS
| Coefficient 95% CI Coefficient 95% CI Coefficient 95% CI
---------------+--------------------------------------------------------------------------------------------------------
None | 1 1 1
CPS Only | 2.520022 1.51719 4.185707 .8276127 .5026645 1.362624 .9414855 .5585413 1.586982
CLS Only | 1.563043 .8702346 2.807409 2.539109 1.550092 4.159157 1.702195 .9964641 2.90775
Both CPS & CLS | 1.258737 .7289055 2.173697 .725354 .4359374 1.206913 1.685971 1.036719 2.741821
White | 1 1 1
Black | 1.173601 .7306474 1.885094 1.155772 .7457687 1.791183 1.434602 .9018611 2.282039
Hispanic | .9474532 .5989693 1.498687 .6523108 .4211421 1.01037 1.218457 .7832058 1.89559
------------------------------------------------------------------------------------------------------------------------The list of variables on the left is missing the names of the factor variables. Turn them on and stack them:
collect style header exposure race, title(label)
collect style row stack, nobinder
collect preview
--------------------------------------------------------------------------------------------------------------------------
| CPS_Only CLS_Only Both_CPS___CLS
| Coefficient 95% CI Coefficient 95% CI Coefficient 95% CI
-----------------+--------------------------------------------------------------------------------------------------------
System Exposure |
None | 1 1 1
CPS Only | 2.520022 1.51719 4.185707 .8276127 .5026645 1.362624 .9414855 .5585413 1.586982
CLS Only | 1.563043 .8702346 2.807409 2.539109 1.550092 4.159157 1.702195 .9964641 2.90775
Both CPS & CLS | 1.258737 .7289055 2.173697 .725354 .4359374 1.206913 1.685971 1.036719 2.741821
Race |
White | 1 1 1
Black | 1.173601 .7306474 1.885094 1.155772 .7457687 1.791183 1.434602 .9018611 2.282039
Hispanic | .9474532 .5989693 1.498687 .6523108 .4211421 1.01037 1.218457 .7832058 1.89559
--------------------------------------------------------------------------------------------------------------------------You don’t need the base categories:`
collect style showbase off
collect preview
--------------------------------------------------------------------------------------------------------------------------
| CPS_Only CLS_Only Both_CPS___CLS
| Coefficient 95% CI Coefficient 95% CI Coefficient 95% CI
-----------------+--------------------------------------------------------------------------------------------------------
System Exposure |
CPS Only | 2.520022 1.51719 4.185707 .8276127 .5026645 1.362624 .9414855 .5585413 1.586982
CLS Only | 1.563043 .8702346 2.807409 2.539109 1.550092 4.159157 1.702195 .9964641 2.90775
Both CPS & CLS | 1.258737 .7289055 2.173697 .725354 .4359374 1.206913 1.685971 1.036719 2.741821
Race |
Black | 1.173601 .7306474 1.885094 1.155772 .7457687 1.791183 1.434602 .9018611 2.282039
Hispanic | .9474532 .5989693 1.498687 .6523108 .4211421 1.01037 1.218457 .7832058 1.89559
--------------------------------------------------------------------------------------------------------------------------You don’t need this many digits: three will be plenty, and you can do that with nformat(). Normally the maximum amount of digits in the format doesn’t matter much, but in this case Stata will reserve that many spaces for the upper bound of the confidence interval. So instead of using %8.3f, use %5.3f so there are no extra spaces.
You also want to put the confidence intervals in square brackets, which can be done with sformat(). Recall that in defining an sformat, the value itself is %s. To put a dash between the upper and lower bounds of the confidence interval, use cidelimiter().
collect style cell result, nformat(%5.3f)
collect style cell result[_r_ci], sformat("[%s]") cidelimiter("-")
collect preview
-----------------------------------------------------------------------------------------------------------
| CPS_Only CLS_Only Both_CPS___CLS
| Coefficient 95% CI Coefficient 95% CI Coefficient 95% CI
-----------------+-----------------------------------------------------------------------------------------
System Exposure |
CPS Only | 2.520 [1.517-4.186] 0.828 [0.503-1.363] 0.941 [0.559-1.587]
CLS Only | 1.563 [0.870-2.807] 2.539 [1.550-4.159] 1.702 [0.996-2.908]
Both CPS & CLS | 1.259 [0.729-2.174] 0.725 [0.436-1.207] 1.686 [1.037-2.742]
Race |
Black | 1.174 [0.731-1.885] 1.156 [0.746-1.791] 1.435 [0.902-2.282]
Hispanic | 0.947 [0.599-1.499] 0.652 [0.421-1.010] 1.218 [0.783-1.896]
-----------------------------------------------------------------------------------------------------------Next let’s improve the column headers. Add an explanatory title above the outcomes by adding a label to the coleq dimension and then show it:
collect label dim coleq "System involvement (ref: none)", modify
collect style header coleq, title(label) The label for the levels of coleq also need improvement. Add the number of observations for each outcome like in the previous chapter:
count if involvement==1
local n1 = r(N)
count if involvement==2
local n2 = r(N)
count if involvement==3
local n3 = r(N)
collect label levels coleq CPS_Only "CPS Only (N=`n1')" CLS_Only "CLS_Only (N=`n2')" Both_CPS___CLS "Both CPS & CLS (N=`n3')", modify 225
309
261Finally, relabel the relevant levels of result to say you are using relative risk ratios (RRR) rather than coefficients.
collect label levels result _r_b "RRR" _r_ci "95% CI", modify
collect preview
--------------------------------------------------------------------------------------------
| System involvement (ref: none)
| CPS Only (N=225) CLS_Only (N=309) Both CPS & CLS (N=261)
| RRR 95% CI RRR 95% CI RRR 95% CI
-----------------+--------------------------------------------------------------------------
System Exposure |
CPS Only | 2.520 [1.517-4.186] 0.828 [0.503-1.363] 0.941 [0.559-1.587]
CLS Only | 1.563 [0.870-2.807] 2.539 [1.550-4.159] 1.702 [0.996-2.908]
Both CPS & CLS | 1.259 [0.729-2.174] 0.725 [0.436-1.207] 1.686 [1.037-2.742]
Race |
Black | 1.174 [0.731-1.885] 1.156 [0.746-1.791] 1.435 [0.902-2.282]
Hispanic | 0.947 [0.599-1.499] 0.652 [0.421-1.010] 1.218 [0.783-1.896]
--------------------------------------------------------------------------------------------Add stars for significance, a note explaining them, and a title for the table:
collect style cell result[_r_b], sformat("%s ")
collect stars _r_p .001 "***" .01 "** " .05 "* " .1 "+ " 1 " ", attach(_r_b)
collect note "*** p<.001; ** p<.01; * p<.05; + p<.1."
collect title "Table A. Relative Risk Ratios from Multinomial Logistic Regression of System Involvement on Prior System Exposure"Last of all, remove all the borders. This is done by styling the border_block cells. In the border() option, you can name a specific border or leave it blank to control all borders. To remove a border set its pattern to nil:
collect style cell border_block, border(, pattern(nil))
collect preview
Table A. Relative Risk Ratios from Multinomial Logistic Regression of System Involvement on Prior System Exposure
System involvement (ref: none)
CPS Only (N=225) CLS_Only (N=309) Both CPS & CLS (N=261)
RRR 95% CI RRR 95% CI RRR 95% CI
System Exposure
CPS Only 2.520*** [1.517-4.186] 0.828 [0.503-1.363] 0.941 [0.559-1.587]
CLS Only 1.563 [0.870-2.807] 2.539*** [1.550-4.159] 1.702+ [0.996-2.908]
Both CPS & CLS 1.259 [0.729-2.174] 0.725 [0.436-1.207] 1.686* [1.037-2.742]
Race
Black 1.174 [0.731-1.885] 1.156 [0.746-1.791] 1.435 [0.902-2.282]
Hispanic 0.947 [0.599-1.499] 0.652+ [0.421-1.010] 1.218 [0.783-1.896]
*** p<.001; ** p<.01; * p<.05; + p<.1.