lazarus-ccr/applications/lazstats/source/forms/analysis/multivariate/pathunit.pas

unit PathUnit;

{$mode objfpc}{$H+}

interface

uses
  Classes, SysUtils, FileUtil, LResources, Forms, Controls, Graphics, Dialogs,
  StdCtrls, Buttons, ExtCtrls,
  MainUnit, OutputUnit, Globals, MatrixLib, DataProcs;

type

  { TPathFrm }

  TPathFrm = class(TForm)
    Bevel1: TBevel;
    Panel1: TPanel;
    Panel2: TPanel;
    Panel3: TPanel;
    ResetBtn: TButton;
    CancelBtn: TButton;
    ComputeBtn: TButton;
    ReturnBtn: TButton;
    SaveDialog1: TSaveDialog;
    StatsChk: TCheckBox;
    ModelChk: TCheckBox;
    Reprochk: TCheckBox;
    SaveChk: TCheckBox;
    GroupBox1: TGroupBox;
    ResetModelBtn: TButton;
    CausedInBtn: TBitBtn;
    CausedOutBtn: TBitBtn;
    CausingInBtn: TBitBtn;
    CausingOutBtn: TBitBtn;
    CausedEdit: TEdit;
    Label4: TLabel;
    Label5: TLabel;
    CausingList: TListBox;
    ModelNo: TEdit;
    InBtn: TBitBtn;
    Label3: TLabel;
    OutBtn: TBitBtn;
    Label1: TLabel;
    Label2: TLabel;
    VarList: TListBox;
    ScrollBar: TScrollBar;
    ListBox1: TListBox;
    procedure CancelBtnClick(Sender: TObject);
    procedure CausedInBtnClick(Sender: TObject);
    procedure CausedOutBtnClick(Sender: TObject);
    procedure CausingInBtnClick(Sender: TObject);
    procedure CausingOutBtnClick(Sender: TObject);
    procedure ComputeBtnClick(Sender: TObject);
    procedure FormActivate(Sender: TObject);
    procedure FormCreate(Sender: TObject);
    procedure FormShow(Sender: TObject);
    procedure InBtnClick(Sender: TObject);
    procedure OutBtnClick(Sender: TObject);
    procedure ResetBtnClick(Sender: TObject);
    procedure ResetModelBtnClick(Sender: TObject);
    procedure ReturnBtnClick(Sender: TObject);
    procedure ScrollBarChange(Sender: TObject);
  private
    { private declarations }
    FAutoSized: Boolean;
    Model : integer;
    ModelDefined : BoolDyneVec;
    causedseq : IntDyneVec;
    nocausing : IntDyneVec;
    causingseq : IntDyneMat;
    NoModels : integer;
  public
    { public declarations }
  end; 

var
  PathFrm: TPathFrm;

implementation

uses
  Math;

{ TPathFrm }

procedure TPathFrm.ResetBtnClick(Sender: TObject);
VAR i : integer;
begin
     if causingseq = nil then SetLength(causingseq,NoVariables,NoVariables);
     if ModelDefined = nil then SetLength(ModelDefined,NoVariables);
     if nocausing = nil then SetLength(nocausing,NoVariables);
     if causedseq = nil then SetLength(causedseq,NoVariables);
     ListBox1.Clear;
     CausingList.Clear;
     VarList.Clear;
     OutBtn.Enabled := false;
     InBtn.Enabled := true;
     CausedOutBtn.Enabled := false;
     CausedInBtn.Enabled := true;
     CausingInBtn.Enabled := true;
     CausingOutBtn.Enabled := false;
     ModelNo.Text := '1';
     ScrollBar.Position := 1;
     CausedEdit.Text := '';
     StatsChk.Checked := true;
     ModelChk.Checked := true;
     ReproChk.Checked := true;
     SaveChk.Checked := false;
     NoModels := 0;
     for i := 1 to NoVariables do
         ListBox1.Items.Add(OS3MainFrm.DataGrid.Cells[i,0]);
     for i := 1 to NoVariables do ModelDefined[i-1] := false;
end;

procedure TPathFrm.ResetModelBtnClick(Sender: TObject);
VAR i : integer;
begin
     Model := ScrollBar.Position;
     if CausedEdit.Text <> '' then CausedOutBtnClick(self);
     if CausingList.Items.Count > 0 then CausingList.Clear;
     causedseq[Model-1] := 0;
     nocausing[Model-1] := 0;
     for i := 1 to nocausing[Model-1] do causingseq[Model-1,i-1] := 0;
     ModelDefined[Model-1] := false;
end;

procedure TPathFrm.ReturnBtnClick(Sender: TObject);
begin
     causedseq := nil;
     nocausing := nil;
     causingseq := nil;
     ModelDefined := nil;
     Close;
end;

procedure TPathFrm.ScrollBarChange(Sender: TObject);
var
   i, j, col : integer;
   cellstring : string;
begin
     ScrollBar.Max := NoVariables + 1;
     if ScrollBar.Position > NoVariables then
     begin
          ScrollBar.Position := NoVariables;
          exit;
     end;
     if ScrollBar.Position > NoModels then
     begin
          if (CausedEdit.Text <> '') and (CausingList.Items.Count > 0) then
          begin // save model information
               Model := ScrollBar.Position - 1;
               ModelDefined[Model-1] := true;
               nocausing[Model-1] := CausingList.Items.Count;
               NoModels := NoModels + 1;
               for i := 1 to NoVariables do
               begin
                    cellstring := OS3MainFrm.DataGrid.Cells[i,0];
                    if cellstring = CausedEdit.Text then causedseq[Model-1] := i;
                    for j := 0 to CausingList.Items.Count - 1 do
                    begin
                         if cellstring = CausingList.Items.Strings[j] then
                            causingseq[Model-1,j] := i;
                    end;
               end;
               CausingList.Clear;
               CausedEdit.Text := '';
               CausedInBtn.Enabled := true;
               CausedOutBtn.Enabled := false;
               CausingInBtn.Enabled := true;
               CausingOutBtn.Enabled := false;
          end;
     end;

     if ScrollBar.Position <> Model then
     begin
          CausingList.Clear;
          ModelNo.Text := IntToStr(ScrollBar.Position);
          Model := ScrollBar.Position;
          CausedEdit.Text := '';
          if ModelDefined[Model-1] then // model exists - reload data
          begin
               col := causedseq[Model-1];
               if col <> 0 then
               begin
                  CausedEdit.Text := OS3MainFrm.DataGrid.Cells[col,0];
                  CausingList.Clear;
               end
               else
               begin
                    CausedEdit.Text := '';
                    CausingList.Clear;
                    exit;
               end;
               for i := 1 to nocausing[Model-1] do
               begin
                    col := causingseq[Model-1,i-1];
                    cellstring := OS3MainFrm.DataGrid.Cells[col,0];
                    CausingList.Items.Add(cellstring);
               end;
          end;
     end;
end;

procedure TPathFrm.FormActivate(Sender: TObject);
var
  w: Integer;
begin
  if FAutoSized then
    exit;

  w := MaxValue([ResetBtn.Width, CancelBtn.Width, ComputeBtn.Width, ReturnBtn.Width]);
  ResetBtn.Constraints.MinWidth := w;
  CancelBtn.Constraints.MinWidth := w;
  ComputeBtn.Constraints.MinWidth := w;
  ReturnBtn.Constraints.MinWidth := w;
  Constraints.MinWidth := Width;
  Constraints.MinHeight := Height;

  FAutoSized := true;
end;

procedure TPathFrm.FormCreate(Sender: TObject);
begin
  Assert(OS3MainFrm <> nil);
  if OutputFrm = nil then
    Application.CreateForm(TOutputFrm, OutputFrm);
end;

procedure TPathFrm.FormShow(Sender: TObject);
begin
     causedseq := nil;
     nocausing := nil;
     causingseq := nil;
     ModelDefined := nil;
     ResetBtnClick(self);
end;

procedure TPathFrm.InBtnClick(Sender: TObject);
VAR i, index : integer;
begin
     index := ListBox1.Items.Count;
     i := 0;
     while i < index do
     begin
         if (ListBox1.Selected[i]) then
         begin
            VarList.Items.Add(ListBox1.Items.Strings[i]);
            ListBox1.Items.Delete(i);
            index := index - 1;
            i := 0;
         end
         else i := i + 1;
     end;
     OutBtn.Enabled := true;
end;

procedure TPathFrm.OutBtnClick(Sender: TObject);
VAR index : integer;
begin
     index := VarList.ItemIndex;
     if index < 0 then
     begin
          OutBtn.Enabled := false;
          exit;
     end;
     VarList.Items.Delete(index);
end;

procedure TPathFrm.CancelBtnClick(Sender: TObject);
begin
     causedseq := nil;
     nocausing := nil;
     causingseq := nil;
     ModelDefined := nil;
     Close;
end;

procedure TPathFrm.CausedInBtnClick(Sender: TObject);
VAR index : integer;
begin
     index := VarList.ItemIndex;
     CausedEdit.Text := VarList.Items.Strings[index];
     CausedOutBtn.Enabled := true;
     CausedInBtn.Enabled := false;
end;

procedure TPathFrm.CausedOutBtnClick(Sender: TObject);
begin
     CausedEdit.Text := '';
     CausedOutBtn.Enabled := false;
     CausedInBtn.Enabled := true;
end;

procedure TPathFrm.CausingInBtnClick(Sender: TObject);
VAR i, index : integer;
begin
     index := VarList.Items.Count;
     for i := 0 to index-1 do
     begin
         if (VarList.Selected[i]) then
            CausingList.Items.Add(VarList.Items.Strings[i]);
     end;
     CausingOutBtn.Enabled := true;
end;

procedure TPathFrm.CausingOutBtnClick(Sender: TObject);
VAR index : integer;
begin
     index := CausingList.ItemIndex;
     if index < 0 then
     begin
          CausingOutBtn.Enabled := false;
          exit;
     end;
     CausingList.Items.Delete(index);
end;

procedure TPathFrm.ComputeBtnClick(Sender: TObject);
var
   i, j, k, col, row, NoVars, nocaused, NoSelected, NoIndepVars : integer;
   count, IER, noexogenous, t, L: integer;
   constant, StdErrEst, ProbOut, R2, Temp, d2, sum, absdiff : double;
   cellstring, outline : string;
   ColNoSelected, selected : IntDyneVec;
   IndepIndex : IntDyneVec;
   rmat, WorkMat, PathCoef, IndMatrix, InvMatrix, e, W : DblDyneMat;
   means, variances, stddevs, beta, p : DblDyneVec;
   zvals : DblDyneMat; // z scores for path model
   genedz : IntDyneVec; // list of z's created for path models
   causal : IntDyneMat;
   exogenous : IntDyneVec;
   RowLabels, ColLabels, Labels: StrDyneVec;
   title : string;
   matched : boolean;
   prtopt : boolean;
   errorcode : boolean = false;
   done : boolean;
   zscore : double;
begin
    if NoModels < ScrollBar.Position then
    begin
         Model := ScrollBar.Position;
         ModelDefined[Model-1] := true;
         nocausing[Model-1] := CausingList.Items.Count;
         NoModels := NoModels + 1;
         for i := 1 to NoVariables do
         begin
              cellstring := OS3MainFrm.DataGrid.Cells[i,0];
              if cellstring = CausedEdit.Text then causedseq[Model-1] := i;
              for j := 0 to CausingList.Items.Count - 1 do
              begin
                   if cellstring = CausingList.Items.Strings[j] then
                            causingseq[Model-1,j] := i;
              end;
         end;
         CausingList.Clear;
         CausedEdit.Text := '';
         CausedInBtn.Enabled := true;
         CausedOutBtn.Enabled := false;
         CausingInBtn.Enabled := true;
         CausingOutBtn.Enabled := false;
    end;

    nocaused := NoModels;
    SetLength(rmat,NoVariables+1,NoVariables+1);
    SetLength(WorkMat,NoVariables+1,NoVariables+1);
    SetLength(PathCoef,NoVariables,NoVariables);
    SetLength(IndMatrix,NoVariables,NoVariables);
    SetLength(InvMatrix,NoVariables,NoVariables);
    SetLength(e,NoVariables,NoVariables);
    SetLength(W,NoVariables,NoVariables);
    SetLength(means,NoVariables);
    SetLength(variances,NoVariables);
    SetLength(stddevs,NoVariables);
    SetLength(beta,NoVariables);
    SetLength(p,NoVariables*NoVariables);
    SetLength(Causal,2,NoVariables*NoVariables);
    SetLength(RowLabels,NoCases);
    SetLength(ColLabels,NoVariables);
    SetLength(Labels,NoVariables);
    SetLength(IndepIndex,NoVariables);
    SetLength(exogenous,NoVariables);
    SetLength(ColNoSelected,NoVariables);
    SetLength(selected,NoVariables);
    SetLength(zvals,NoCases,NoVariables);
    SetLength(genedz,NoVariables);

    // get and show model parameters
    OutputFrm.RichEdit.Clear;
    OutputFrm.RichEdit.Lines.Add('PATH ANALYSIS RESULTS');
    OutputFrm.RichEdit.Lines.Add('');

    for i := 1 to nocaused do
    begin
        col := causedseq[i-1];
        outline := 'CAUSED VARIABLE: ';
        outline := outline + OS3MainFrm.DataGrid.Cells[col,0];
        OutputFrm.RichEdit.Lines.Add(outline);
        OutputFrm.RichEdit.Lines.Add('     Causing Variables:');
        for j := 1 to nocausing[i-1] do
        begin
            col := causingseq[i-1,j-1];
            outline := '    ';
            outline := outline + OS3MainFrm.DataGrid.Cells[col,0];
            OutputFrm.RichEdit.Lines.Add(outline);
        end;
    end;
    OutputFrm.ShowModal;
    OutputFrm.RichEdit.Clear;

    // get correlations among all variables selected for the analysis
    NoSelected := VarList.Items.Count;
    for j := 1 to NoVariables do
    begin
        cellstring := OS3MainFrm.DataGrid.Cells[j,0];
        for i := 1 to NoSelected do
        begin
            if cellstring = VarList.Items.Strings[i-1] then
            begin
                 ColNoSelected[i-1] := j;
                 RowLabels[i-1] := cellstring;
            end;
        end;
    end;
    count := NoCases;
    Correlations(NoSelected,ColNoSelected,rmat,means,variances,stddevs, errorcode,count);
    if SaveChk.Checked then
    begin
         SaveDialog1.Filter := 'Matrix files (*.MAT)|*.MAT|All files (*.*)|*.*';
         SaveDialog1.FilterIndex := 1;
         SaveDialog1.Execute;
         MATSAVE(rmat,NoSelected,NoSelected,means,stddevs,count,RowLabels,
               RowLabels,SaveDialog1.FileName);
    end;

    if StatsChk.Checked then
    begin
         title := 'Correlation Matrix';
         MAT_PRINT(rmat,NoSelected,NoSelected,title,RowLabels,RowLabels,count);
         title := 'MEANS';
         DynVectorPrint(means,NoSelected,title,RowLabels,count);
         title := 'VARIANCES';
         DynVectorPrint(variances,NoSelected,title,RowLabels,count);
         title := 'STANDARD DEVIATIONS';
         DynVectorPrint(stddevs,NoSelected,title,RowLabels,count);
         OutputFrm.ShowModal;
         OutputFrm.RichEdit.Clear;
    end;

    // initialize reconstruction matrix, weights matrix and path coefficients
    for i := 0 to NoSelected-1 do
    begin
        for j := 0 to NoSelected-1 do
        begin
            e[i,j] := 0.0;
            W[i,j] := 0.0;
            PathCoef[i,j] := 0.0;
        end;
    end;

    //Now, do the regression analysis for each model
    for i := 1 to nocaused do
    begin
         NoVars := nocausing[i-1] + 1;
         for j := 1 to nocausing[i-1] do
         begin
              col := causingseq[i-1,j-1];
              IndepIndex[j-1] := j; // independents
              selected[j-1] := col;
              Labels[j-1] := OS3MainFrm.DataGrid.Cells[col,0];
         end;
         row := causedseq[i-1]; //sequence no. of caused variable
         IndepIndex[NoVars-1] := row; // dependent
         selected[NoVars-1] := row;
         Labels[NoVars-1] := OS3MainFrm.DataGrid.Cells[row,0];

         // get correlation matrix for this model
         Correlations(NoVars,selected,WorkMat,means,variances,stddevs,
                      errorcode,count);
         if ModelChk.Checked then
         begin
              OutputFrm.RichEdit.Lines.Add('');
              outline := format('Dependent Variable = %s',[OS3MainFrm.DataGrid.Cells[row,0]]);
              OutputFrm.RichEdit.Lines.Add(outline);
              OutputFrm.RichEdit.Lines.Add('');
              title := 'Correlation Matrix';
              MAT_PRINT(WorkMat,NoVars,NoVars,title,Labels,Labels,count);
              title := 'MEANS';
              DynVectorPrint(means,NoVars,title,Labels,count);
              title := 'VARIANCES';
              DynVectorPrint(variances,NoVars,title,Labels,count);
              title := 'STANDARD DEVIATIONS';
              DynVectorPrint(stddevs,NoVars,title,Labels,count);
              OutputFrm.ShowModal;
              OutputFrm.RichEdit.Clear;
         end;

         // Get regression analysis for this model
         ProbOut := 0.999;
         NoIndepVars := NoVars - 1;
         if StatsChk.Checked then
         begin
              OutputFrm.RichEdit.Lines.Add('');
              outline := format('Dependent Variable = %s',[OS3MainFrm.DataGrid.Cells[row,0]]);
              OutputFrm.RichEdit.Lines.Add(outline);
              OutputFrm.RichEdit.Lines.Add('');
         end;
         if StatsChk.Checked then prtopt := true else prtopt := false;
         MReg2(count,NoVars,NoIndepVars,IndepIndex,WorkMat,IndMatrix,
               Labels,R2,beta,means,variances,IER,StdErrEst,constant,
               ProbOut,prtopt,false,false, OutputFrm.RichEdit.Lines);
         if prtopt then
         begin
              OutputFrm.RichEdit.Lines.Add('');
              OutputFrm.ShowModal;
              OutputFrm.RichEdit.Clear;
         end;

         for j := 1 to nocausing[i-1] do
         begin
              col := causingseq[i-1,j-1];
              PathCoef[row-1,col-1] := beta[j-1];
         end;
    end; // next i (caused regressions)

    //Now, reconstruct the correlation matrix from path coefficients
    //First, obtain list of exogenous variables
    noexogenous := 0;
    for i := 1 to NoSelected do
    begin
        matched := false;
        col := ColNoSelected[i-1];
        for j := 1 to nocaused do
            if (causedseq[j-1] = col) then matched := true;
        if ( not matched) then
        begin
            exogenous[noexogenous] := col;
            noexogenous := noexogenous + 1;
        end;
    end;

    // transform raw scores to z scores for exogenous variables
    Correlations(NoSelected,ColNoSelected,rmat,means,variances,stddevs,
                 errorcode,count);
    for i := 1 to noselected do genedz[i-1] := 0; // initialize
    for k := 1 to noexogenous do
    begin
         col := exogenous[k-1];
         for j := 1 to noselected do
         begin // find position of corresponding mean and std.dev.
              if ColNoSelected[j-1] = col then row := j;
         end;
         for i := 1 to NoCases do
         begin
              zvals[i-1,col-1] := StrToFloat(OS3MainFrm.DataGrid.Cells[col,i]);
              zvals[i-1,col-1] := (zvals[i-1,col-1] - means[row-1]) / stddevs[row-1];
              RowLabels[i-1] := format('Subject %d',[i]);
         end;
         genedz[col-1] := 1; // mark as generated
    end;
{
    // print matrix of path z scores for exogenous variables
    title := 'Data Array of Subject exogenous z Scores';
    MAT_PRINT(zvals,NoCases,NoSelected,title,RowLabels,ColLabels,NoCases);
    OutputFrm.ShowModal;
    OutputFrm.RichEdit.Clear;
}

    for i := 1 to NoVariables do
    begin
         cellstring := OS3MainFrm.DataGrid.Cells[i,0];
         for j := 1 to NoSelected do
         begin
              if cellstring = VarList.Items.Strings[j-1] then
              begin
                   RowLabels[i-1] := cellstring;
                   ColLabels[i-1] := cellstring;
              end;
         end;
    end;

    //Build matrix of path coefficients
    for i := 1 to nocaused do
    begin
        row := causedseq[i-1];
        for j := 1 to nocausing[i-1] do
        begin
            col := causingseq[i-1,j-1];
            W[row-1,col-1] := PathCoef[row-1,col-1];
        end;
    end;

    //Print results
    if StatsChk.Checked then
    begin
         title := 'Matrix of Path Coefficients in Rows';
         MAT_PRINT(W,NoSelected,NoSelected,title,ColLabels,ColLabels,count);
         OutputFrm.ShowModal;
         OutputFrm.RichEdit.Clear;
    end;

    //Build models vectors
    k := 0;
    for i := 1 to nocaused do
    begin
        for j := 1 to nocausing[i-1] do
        begin
            k := k + 1;
            causal[0,k-1] := causedseq[i-1];
            causal[1,k-1] := causingseq[i-1,j-1];
            row := causedseq[i-1];
            col := causingseq[i-1,j-1];
            p[k-1] := PathCoef[row-1,col-1];
        end;
    end;
    NoModels := k;

    //Sort on resultant then causing variables
    for i := 1 to NoModels - 1 do
    begin
        for j := i + 1 to NoModels do
        begin
            if (causal[0,i-1] > causal[0,j-1]) then // swap
            begin
                t := causal[0,i-1];
                causal[0,i-1] := causal[0,j-1];
                causal[0,j-1] := t;
                t := causal[1,i-1];
                causal[1,i-1] := causal[1,j-1];
                causal[1,j-1] := t;
                Temp := p[i-1];
                p[i-1] := p[j-1];
                p[j-1] := Temp;
            end;
        end;
    end;
    for i := 1 to NoModels - 1 do
    begin
        for j := i + 1 to NoModels do
        begin
            if ((causal[0,i-1] = causal[0,j-1]) and (causal[1,i-1] > causal[1,j-1])) then
            begin
                t := causal[0,i-1];
                causal[0,i-1] := causal[0,j-1];
                causal[0,j-1] := t;
                t := causal[1,i-1];
                causal[1,i-1] := causal[1,j-1];
                causal[1,j-1] := t;
                Temp := p[i-1];
                p[i-1] := p[j-1];
                p[j-1] := Temp;
            end;
        end;
    end;

    OutputFrm.RichEdit.Lines.Add('SUMMARY OF CAUSAL MODELS');
    OutputFrm.RichEdit.Lines.Add('Var. Caused    Causing Var.  Path Coefficient');

    for i := 1 to NoModels do
    begin
        outline := format('%12s   %12s  %6.3f',
                [OS3MainFrm.DataGrid.Cells[causal[0,i-1],0],
                OS3MainFrm.DataGrid.Cells[causal[1,i-1],0],
                p[i-1]]);
        OutputFrm.RichEdit.Lines.Add(outline);
    end;
    OutputFrm.RichEdit.Lines.Add('');
    OutputFrm.ShowModal;
    OutputFrm.RichEdit.Clear;

    //Get reproduced correlation matrix in e
    done := false;
    while not done do
    begin
         for i := 1 to nocaused do // check each caused for use of existing z values
         begin
              for j := 1 to nocausing[i-1] do
              begin
                   count := 0;
                   for L := 1 to noselected do
                   begin
                        if genedz[L-1] = 1 then count := count + 1;
                   end;
              end;
              if count >= nocausing[i-1] then // calculate path z
              begin
                   row := causedseq[i-1]; // generation z column & row of path coef.
                   for j := 1 to nocausing[i-1] do
                   begin  // sum of Path coefficients times corresponding z's
                        col := causingseq[i-1,j-1]; // column of path coefficient
                        for k := 1 to NoCases do
                        begin
                             zscore := zvals[k-1,col-1]; // causing z score
                             zvals[k-1,row-1] := zvals[k-1,row-1] + zscore * PathCoef[row-1,col-1];
                        end;
                   end;
                   genedz[row-1] := 1; // mark as generated
              end; // if count equals no. of causing variables
              count := 0; // check for completion of all z's
              for j := 1 to noselected do
                  if genedz[j-1] = 1 then count := count + 1;
              if count = noselected then done := true;
         end; // next i caused variable
    end; // while not done

    // print matrix of path z scores
    for i := 1 to NoCases do RowLabels[i-1] := format('Subject %d',[i]);
    title := 'Data Array of Subject Path z Scores';
    MAT_PRINT(zvals,NoCases,NoSelected,title,RowLabels,ColLabels,NoCases);
    OutputFrm.ShowModal;
    OutputFrm.RichEdit.Clear;

    // now calculate the correlation among the generated z values
    for i := 1 to noselected do
    begin // initialize arrays
         for j := 1 to noselected do
         begin
              e[i-1,j-1] := 0.0;
         end;
         means[i-1] := 0.0;
         stddevs[i-1] := 0.0;
    end;
    for k := 1 to NoCases do
    begin
         for i := 1 to noselected do
         begin
              for j := 1 to noselected do
              begin
                   e[i-1,j-1] := e[i-1,j-1] + zvals[k-1,i-1] * zvals[k-1,j-1];
              end;
              means[i-1] := means[i-1] + zvals[k-1,i-1];
              stddevs[i-1] := stddevs[i-1] + (zvals[k-1,i-1] * zvals[k-1,i-1]);
         end;
    end;
    for i := 1 to noselected do
    begin
         stddevs[i-1] := stddevs[i-1] - (means[i-1] * means[i-1] / NoCases);
         stddevs[i-1] := stddevs[i-1] / (NoCases - 1);
         stddevs[i-1] := sqrt(stddevs[i-1]);
         for j := 1 to noselected do
         begin // covariances
              e[i-1,j-1] := e[i-1,j-1] - (means[i-1] * means[j-1] / NoCases);
              e[i-1,j-1] := e[i-1,j-1] / (NoCases - 1);
         end;
         means[i-1] := means[i-1] / NoCases;
    end;
    for i := 1 to noselected do
    begin
         for j := 1 to noselected do
         begin
              e[i-1,j-1] := e[i-1,j-1] / (stddevs[i-1]*stddevs[j-1]);
         end;
    end;

    if (ReproChk.Checked) then
    begin
       title := 'Reproduced Correlation Matrix';
       MAT_PRINT(e,NoSelected,NoSelected,title,ColLabels,ColLabels,count);
    end;

    //Examine discrepencies
    d2 := 0.0;
    sum := 0.0;
    for i := 1 to NoSelected do
    begin
        for j := 1 to NoSelected do
        begin
            absdiff := abs(rmat[i-1,j-1] - e[i-1,j-1]);
            sum := sum + absdiff;
            if (absdiff > d2) then d2 := absdiff;
        end;
    end;

    OutputFrm.RichEdit.Lines.Add('Average absolute difference between observed and reproduced');
    outline := format('coefficients := %5.3f',[sum / (NoSelected * NoSelected)]);
    OutputFrm.RichEdit.Lines.Add(outline);
    outline := format('Maximum difference found := %5.3f',[d2]);
    OutputFrm.RichEdit.Lines.Add(outline);
    OutputFrm.ShowModal;

    // clean up heap (delete last allocated first)
    genedz := nil;
    zvals := nil;
    selected := nil;
    ColNoSelected := nil;
    exogenous := nil;
    IndepIndex := nil;
    Labels := nil;
    ColLabels := nil;
    RowLabels := nil;
    Causal := nil;
    p := nil;
    beta := nil;
    stddevs := nil;
    variances := nil;
    means := nil;
    W := nil;
    e := nil;
    InvMatrix := nil;
    IndMatrix := nil;
    PathCoef := nil;
    WorkMat := nil;
    rmat := nil;
end;


initialization
  {$I pathunit.lrs}

end.