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    If you have Stata 17 or newer, you can use the collect with
    cpcorr to build your table for LaTeX. One challenge here is that
    cpcorr does not apply the same row and column names of
    r(C) to r(p), so I had to write a short (byable)
    wrap-around program to accomplish this. Also the example data does not
    have labels on the variables, but if it did, then those labels would
    show up in the table instead of the variable names.

    Here is the code I used.
    Code:
    program mod_cpcorr, rclass byable(recall)
        syntax anything [if] [in] [, *]
        marksample touse
        cpcorr `anything' if `touse', `options'
        tempname C p
        matrix `C' = r(C)
        matrix `p' = r(p)
        matrix colname `p' = `:colfullname `C', quote'
        matrix rowname `p' = `:rowfullname `C', quote'
        return scalar N = r(N)
        return matrix C = `C'
        return matrix p = `p'
    end
    
    sort group
    
    by group : ///
        collect corr=(r(C)) pvalue=(r(p)) : ///
        mod_cpcorr fd ka ext dom pr la \ ///
            type1 type2 indicator1 decade1 decade2 decade3
    by group : ///
        collect cov=(r(C)) : ///
        mod_cpcorr fd ka ext dom pr la \ ///
            type1 type2 indicator1 decade1 decade2 decade3, covariance
    
    * apply some style choices on the results of interest
    collect style cell result[cov], sformat("(%s)")
    collect style cell result[corr cov] , nformat(%12.2f)
    collect style cell result[pvalue] , nformat(%5.3f)
    * define composite result named show
    collect composite define show = corr cov pvalue, trim
    * hide result names from the header
    collect style header result, level(hide)
    * add note detailing the cell contents
    collect notes "Correlations, (covariances), and p-values."
    
    collect layout (group#rowname) (colname#result[show])
    
    collect export table.tex, replace
    Here is the table.
    Code:
    . collect layout (group#rowname) (colname#result[show])
    
    Collection: default
          Rows: group#rowname
       Columns: colname#result[show]
       Table 1: 28 x 6
    
    ---------------------------------------------------------------------------------------------------------------------
          |          type1          type2          indicator1             decade1             decade2             decade3
    ------+--------------------------------------------------------------------------------------------------------------
    A     |
      fd  | . (0.00) 1.000 . (0.00) 1.000   0.06 (0.08) 0.798 -0.83 (-0.06) 0.000   0.29 (0.02) 0.175   0.47 (0.04) 0.022
      ka  | . (0.00) 1.000 . (0.00) 1.000 -0.30 (-1.69) 0.150   0.19 (0.05) 0.386 -0.15 (-0.05) 0.490 -0.02 (-0.00) 0.943
      ext | . (0.00) 1.000 . (0.00) 1.000 -0.76 (-0.72) 0.000 -0.37 (-0.02) 0.073 -0.04 (-0.00) 0.846   0.39 (0.02) 0.063
      dom | . (0.00) 1.000 . (0.00) 1.000 -0.12 (-0.08) 0.578 -0.76 (-0.02) 0.000   0.52 (0.02) 0.009   0.16 (0.01) 0.456
      pr  | . (0.00) 1.000 . (0.00) 1.000 -0.35 (-1.01) 0.096 -0.91 (-0.13) 0.000   0.10 (0.02) 0.648   0.73 (0.12) 0.000
      la  | . (0.00) 1.000 . (0.00) 1.000   0.65 (0.79) 0.001   0.26 (0.02) 0.214 -0.15 (-0.01) 0.485 -0.09 (-0.01) 0.692
    B     |
      fd  | . (0.00) 1.000 . (0.00) 1.000 -0.37 (-0.06) 0.198 -0.82 (-0.06) 0.000   0.52 (0.04) 0.058   0.32 (0.02) 0.261
      ka  | . (0.00) 1.000 . (0.00) 1.000 -0.46 (-0.24) 0.096 -0.43 (-0.10) 0.127   0.24 (0.05) 0.413   0.20 (0.04) 0.490
      ext | . (0.00) 1.000 . (0.00) 1.000 -0.44 (-0.02) 0.114 -0.37 (-0.01) 0.190   0.21 (0.00) 0.478   0.18 (0.00) 0.549
      dom | . (0.00) 1.000 . (0.00) 1.000 -0.35 (-0.04) 0.222 -0.67 (-0.04) 0.008   0.20 (0.01) 0.497   0.50 (0.03) 0.066
      pr  | . (0.00) 1.000 . (0.00) 1.000 -0.15 (-0.07) 0.621 -0.98 (-0.20) 0.000   0.38 (0.08) 0.185   0.64 (0.12) 0.014
      la  | . (0.00) 1.000 . (0.00) 1.000 -0.30 (-0.01) 0.296 -0.70 (-0.01) 0.005 -0.04 (-0.00) 0.881   0.79 (0.01) 0.001
    C     |
      fd  | . (0.00) 1.000 . (0.00) 1.000 -0.23 (-0.23) 0.525 -0.99 (-0.03) 0.000   0.23 (0.01) 0.524   0.37 (0.02) 0.291
      ka  | . (0.00) 1.000 . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000
      ext | . (0.00) 1.000 . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000
      dom | . (0.00) 1.000 . (0.00) 1.000 -0.40 (-0.27) 0.254 -0.85 (-0.02) 0.002 -0.16 (-0.01) 0.659   0.69 (0.03) 0.028
      pr  | . (0.00) 1.000 . (0.00) 1.000 -0.27 (-0.64) 0.451 -0.97 (-0.08) 0.000   0.12 (0.02) 0.745   0.47 (0.06) 0.166
      la  | . (0.00) 1.000 . (0.00) 1.000 -0.42 (-0.03) 0.228 -0.29 (-0.00) 0.414 -0.13 (-0.00) 0.721   0.31 (0.00) 0.382
    D     |
      fd  | . (0.00) 1.000 . (0.00) 1.000 -0.62 (-0.31) 0.001 -0.96 (-0.05) 0.000   0.44 (0.02) 0.030   0.42 (0.02) 0.040
      ka  | . (0.00) 1.000 . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000
      ext | . (0.00) 1.000 . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000
      dom | . (0.00) 1.000 . (0.00) 1.000 -0.37 (-0.07) 0.077 -0.73 (-0.01) 0.000   0.60 (0.01) 0.002   0.04 (0.00) 0.858
      pr  | . (0.00) 1.000 . (0.00) 1.000 -0.16 (-0.11) 0.467 -0.65 (-0.04) 0.001   0.16 (0.01) 0.467   0.43 (0.03) 0.035
      la  | . (0.00) 1.000 . (0.00) 1.000 -0.34 (-0.11) 0.107 -0.09 (-0.00) 0.687   0.03 (0.00) 0.899   0.05 (0.00) 0.813
    ---------------------------------------------------------------------------------------------------------------------
    Correlations, (covariances), and p-values.
    This table is rather wide, but you can use collect layout to select
    columns and export them separately. For example
    Code:
    . collect layout (group#rowname) (colname[type1 type2]#result[show])
    
    Collection: default
          Rows: group#rowname
       Columns: colname[type1 type2]#result[show]
       Table 1: 28 x 2
    
    -------------------------------------
          |          type1          type2
    ------+------------------------------
    A     |
      fd  | . (0.00) 1.000 . (0.00) 1.000
      ka  | . (0.00) 1.000 . (0.00) 1.000
      ext | . (0.00) 1.000 . (0.00) 1.000
      dom | . (0.00) 1.000 . (0.00) 1.000
      pr  | . (0.00) 1.000 . (0.00) 1.000
      la  | . (0.00) 1.000 . (0.00) 1.000
    B     |
      fd  | . (0.00) 1.000 . (0.00) 1.000
      ka  | . (0.00) 1.000 . (0.00) 1.000
      ext | . (0.00) 1.000 . (0.00) 1.000
      dom | . (0.00) 1.000 . (0.00) 1.000
      pr  | . (0.00) 1.000 . (0.00) 1.000
      la  | . (0.00) 1.000 . (0.00) 1.000
    C     |
      fd  | . (0.00) 1.000 . (0.00) 1.000
      ka  | . (0.00) 1.000 . (0.00) 1.000
      ext | . (0.00) 1.000 . (0.00) 1.000
      dom | . (0.00) 1.000 . (0.00) 1.000
      pr  | . (0.00) 1.000 . (0.00) 1.000
      la  | . (0.00) 1.000 . (0.00) 1.000
    D     |
      fd  | . (0.00) 1.000 . (0.00) 1.000
      ka  | . (0.00) 1.000 . (0.00) 1.000
      ext | . (0.00) 1.000 . (0.00) 1.000
      dom | . (0.00) 1.000 . (0.00) 1.000
      pr  | . (0.00) 1.000 . (0.00) 1.000
      la  | . (0.00) 1.000 . (0.00) 1.000
    -------------------------------------
    Correlations, (covariances), and p-values.
    
    . collect export table_type.tex, replace
    (collection default exported to file table_type.tex)
    
    .
    . collect layout (group#rowname) (colname[indicator1]#result[show])
    
    Collection: default
          Rows: group#rowname
       Columns: colname[indicator1]#result[show]
       Table 1: 28 x 1
    
    ---------------------------
          |          indicator1
    ------+--------------------
    A     |
      fd  |   0.06 (0.08) 0.798
      ka  | -0.30 (-1.69) 0.150
      ext | -0.76 (-0.72) 0.000
      dom | -0.12 (-0.08) 0.578
      pr  | -0.35 (-1.01) 0.096
      la  |   0.65 (0.79) 0.001
    B     |
      fd  | -0.37 (-0.06) 0.198
      ka  | -0.46 (-0.24) 0.096
      ext | -0.44 (-0.02) 0.114
      dom | -0.35 (-0.04) 0.222
      pr  | -0.15 (-0.07) 0.621
      la  | -0.30 (-0.01) 0.296
    C     |
      fd  | -0.23 (-0.23) 0.525
      ka  |      . (0.00) 1.000
      ext |      . (0.00) 1.000
      dom | -0.40 (-0.27) 0.254
      pr  | -0.27 (-0.64) 0.451
      la  | -0.42 (-0.03) 0.228
    D     |
      fd  | -0.62 (-0.31) 0.001
      ka  |      . (0.00) 1.000
      ext |      . (0.00) 1.000
      dom | -0.37 (-0.07) 0.077
      pr  | -0.16 (-0.11) 0.467
      la  | -0.34 (-0.11) 0.107
    ---------------------------
    Correlations, (covariances), and p-values.
    
    . collect export table_ind.tex, replace
    (collection default exported to file table_ind.tex)
    
    .
    . collect layout (group#rowname) (colname[decade1 decade2 decade3]#result[show]
    > )
    
    Collection: default
          Rows: group#rowname
       Columns: colname[decade1 decade2 decade3]#result[show]
       Table 1: 28 x 3
    
    -------------------------------------------------------------------
          |             decade1             decade2             decade3
    ------+------------------------------------------------------------
    A     |
      fd  | -0.83 (-0.06) 0.000   0.29 (0.02) 0.175   0.47 (0.04) 0.022
      ka  |   0.19 (0.05) 0.386 -0.15 (-0.05) 0.490 -0.02 (-0.00) 0.943
      ext | -0.37 (-0.02) 0.073 -0.04 (-0.00) 0.846   0.39 (0.02) 0.063
      dom | -0.76 (-0.02) 0.000   0.52 (0.02) 0.009   0.16 (0.01) 0.456
      pr  | -0.91 (-0.13) 0.000   0.10 (0.02) 0.648   0.73 (0.12) 0.000
      la  |   0.26 (0.02) 0.214 -0.15 (-0.01) 0.485 -0.09 (-0.01) 0.692
    B     |
      fd  | -0.82 (-0.06) 0.000   0.52 (0.04) 0.058   0.32 (0.02) 0.261
      ka  | -0.43 (-0.10) 0.127   0.24 (0.05) 0.413   0.20 (0.04) 0.490
      ext | -0.37 (-0.01) 0.190   0.21 (0.00) 0.478   0.18 (0.00) 0.549
      dom | -0.67 (-0.04) 0.008   0.20 (0.01) 0.497   0.50 (0.03) 0.066
      pr  | -0.98 (-0.20) 0.000   0.38 (0.08) 0.185   0.64 (0.12) 0.014
      la  | -0.70 (-0.01) 0.005 -0.04 (-0.00) 0.881   0.79 (0.01) 0.001
    C     |
      fd  | -0.99 (-0.03) 0.000   0.23 (0.01) 0.524   0.37 (0.02) 0.291
      ka  |      . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000
      ext |      . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000
      dom | -0.85 (-0.02) 0.002 -0.16 (-0.01) 0.659   0.69 (0.03) 0.028
      pr  | -0.97 (-0.08) 0.000   0.12 (0.02) 0.745   0.47 (0.06) 0.166
      la  | -0.29 (-0.00) 0.414 -0.13 (-0.00) 0.721   0.31 (0.00) 0.382
    D     |
      fd  | -0.96 (-0.05) 0.000   0.44 (0.02) 0.030   0.42 (0.02) 0.040
      ka  |      . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000
      ext |      . (0.00) 1.000      . (0.00) 1.000      . (0.00) 1.000
      dom | -0.73 (-0.01) 0.000   0.60 (0.01) 0.002   0.04 (0.00) 0.858
      pr  | -0.65 (-0.04) 0.001   0.16 (0.01) 0.467   0.43 (0.03) 0.035
      la  | -0.09 (-0.00) 0.687   0.03 (0.00) 0.899   0.05 (0.00) 0.813
    -------------------------------------------------------------------
    Correlations, (covariances), and p-values.
    
    . collect export table_decade.tex, replace
    (collection default exported to file table_decade.tex)
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