TableT("file.xls",sheet);

file -  the name of the Excel file which contains the data to be imported.

sheet -  (optional) the name or index of the sheet containing the data (default: 1).

The TableT command imports an Excel file using the ExcelTools package and converts it in the form needed for the use of other commands of the IndependenceModel package, i.e. a list of lists in which every list corresponds to one row of the Excel table.

The Excel table must be constructed in this form: every row corresponds to one variable and contains the name of such variable in the first column followed by all the observations. In this way, every column corresponds to one of the subjects considered in the analysis.

If data is stored with names of the variables on the first row and respective values on the column, use the TableT command followed by the command

ListTools[Transpose](T).

The Excel table cannot have empty cells, because Maple would read them as zeros. So, when the value of an observation is unknown, fill the cell with the value nc.

with(IndependenceModel):

T:=TableT("exemfile.xls");

  T := [["Var 1", 0., 1.0, 0., "nc", 0., 0., 1.0, 1.0, 1.0, 0., 0.,

        0., 1.0, 1.0, 1.0, 0., 0., 0., 1.0, 1.0], ["Var 2", "x", "y",

        "y", "x", "y", "y", "y", "x", "x", "x", "y", "y", "y", "y",

        "x", "y", "x", "x", "x", "y"], ["Var 3", 0., 2.0, 2.0, 2.0,

        0., 0., 2.0, 0., 2.0, 2.0, 2.0, 0., 0., 2.0, 2.0, 0., 0., 2.0,

        0., "nc"], ["Var 4", 1.0, 1.0, 0., 1.0, 0., 0., 1.0, 0., 0.,

        1.0, 1.0, 1.0, 1.0, 1.0, 0., 0., 1.0, 0., 1.0, 1.0], [

        "Var 5", 0., 2.0, 1.0, 1.0, 1.0, 2.0, 2.0, 0., 2.0, 2.0, 0.,

        0., 1.0, 1.0, 0., 0., 2.0, 0., 1.0, 2.0], ["Var 6", "A", "A",

        "B", "A", "B", "A", "B", "A", "B", "B", "A", "B", "B", "B",

        "A", "A", "A", "B", "B", "A"], ["Var 7", 0., 0., 0., 0., 1.0,

        1.0, 0., 0., 1.0, 1.0, 1.0, 1.0, 0., 0., 0., 0., 1.0, 1.0,

        1.0, 0.], ["Var 8", 1.0, 1.0, 0., 1.0, 1.0, 0., 0., 0., 1.0,

        0., 0., 0., "nc", 1.0, 1.0, 1.0, 0., 0., 1.0, 0.], ["Var 9",

        "B", "B", "A", "B", "A", "A", "A", "B", "A", "B", "B", "B",

        "A", "A", "B", "A", "A", "B", "B", "B"], ["Var 10", 0., 2.0,

        1.0, 1.0, 1.0, 2.0, 2.0, 0., 2.0, 2.0, 0., 0., 1.0, 1.0, 0.,

        0., 2.0, 0., 1.0, 2.0]]

LabelT(table);

table - the list of lists containing all the data.

The LabelT command builds a list with the names of the variables, reading them from the table considered. This list corresponds to the first column (or the first row) of the Excel table.

The parameter 'table' can be obtained from an Excel file using the TableT command. If  the table is written directly in Maple by the user, please read the TableT instructions to write it in the correct form.

T:=TableT("exemfile.xls"):

["Var 1", "Var 2", "Var 3", "Var 4", "Var 5", "Var 6", "Var 7", "Var 8", "Var 9", "Var 10"]

NumberOfValues("var", table);

var -  the name of the variable considered

table -  the list of lists containing all the data.

The NumberOfValues command tells how many different values of the variable 'var' occur in the table considered.

The parameter 'table' can be obtained from an Excel file using the TableT command. If  the table is written directly in Maple by the user, please read the TableT instructions to write it in the correct form.

T:=TableT("exemfile.xls"):

NumberOfValues("Var 3",T);

                                                                        2

ListOfValues("var", table);

var -  the name of the variable considered

table -  the list of lists containing all the data.

The ListOfValues command returns the list of the values that the variable 'var' can take, reading them from the table considered.

The parameter 'table' can be obtained from an Excel file using the TableT command. If  the table is written directly in Maple by the user, please read the TableT instructions to write it in the correct form

T:=TableT("exemfile.xls"):

ListOfValues("Var 3",T);

                                                             [0., 2.0]

TableLabel (table , list);

table - the list of lists containing all the data.

list - the list ["var 1", ... , "var n"] with the names of the variables involved in the independence model.

The TableLable command extracts from the table considered the rows corresponding the variables var1, ..., var n of the list. Thus, the output is still a list of lists but contains only n lists.

The parameter 'table' can be obtained from an Excel file using the TableT command. If  the table is written directly in Maple by the user, please read the TableT instructions to write it in the correct form

T:=TableT("exemfile.xls"):

L:=["Var 2","Var 3","Var 6"]

TT:=TableLabel(T,L);

  TT := [["Var 2", "x", "y", "y", "x", "y", "y", "y", "x", "x", "x",

        "y", "y", "y", "y", "x", "y", "x", "x", "x", "y"],

           ["Var 3", 0., 2.0, 2.0, 2.0, 0., 0., 2.0, 0., 2.0, 2.0, 2.0, 0., 0.,

        2.0, 2.0, 0., 0., 2.0, 0., "nc"],

            ["Var 6", "A", "A", "B", "A", "B", "A", "B", "A", "B", "B", "A", "B", "B", "B", "A",

        "A", "A", "B", "B", "A"]]

PossibleObs(table, list);

table -  the list of lists containing all the data.

list - the list ["var 1", ... , "var n"] with the names of the variables involved in the independence model.

The PossibleObs command builds a list of lists containing the possible observation of the variables considered in the parameter 'list'.

For example, considering two different variables with values a or b for the first one and c or d for the second one, the possible observations are (a,c), (a,d), (b,c) and (b,d).

The parameter 'table' can be obtained from an Excel file using the TableT command. If  the table is written directly in Maple by the user, please read the TableT instructions to write it in the correct form

T:=TableT("exemfile.xls"):

Freq(table, list);

table - the list of lists containing all the data.

list - the list ["var 1", ... , "var n"] with the names of the variables involved in the independence model.

The Freq command tells how many times each of the possible observations occurs in the table. The output is a 2-column matrix containing a possible observation in the first column and its frequency in the second one.

The parameter 'table' can be obtained from an Excel file using the TableT command. If  the table is written directly in Maple by the user, please read the TableT instructions to write it in the correct form.

T:=TableT("exemfile.xls"):

L:=["Var 2","Var 3","Var 6"]:

Freq(T,L);

                        [["x", 0., "A"]     3]

                        [["x", 0., "B"]     1]

                        [["x", 2.0, "A"]    2]

                        [["x", 2.0, "B"]    3]

                        [["y", 0., "A"]     2]

                        [["y", 0., "B"]     3]

                        [["y", 2.0, "A"]    2]

                        [["y", 2.0, "B"]    3]

Parametric(table, list, sigma);

table -  the list of lists containing all the data.

list -  the list ["var 1", ... , "var n"] with the names of the variables involved in the independence model.

sigma - the list of lists  [ ["var 1" , ... , "var h"] , ... , ["var k" , ... , "var n"] ] containing the groups of variables of which the user wants to study the independence.

The Parametric command gives the parametric equations of the indipendence model considerd.

The independence model is expressed by the parameters 'list' and 'sigma'.

For example, if we want to study the independence of two variables from a third one, the parameters would be:

list:=["var1" , "var2" , "var3"];  sigma:=[ ["var1", "var2"] , ["var3"] ];.

The parameter 'table' can be obtained from an Excel file using the TableT command. If  the table is written directly in Maple by the user, please read the TableT instructions to write it in the correct form.

T:=TableT("exemfile.xls"):

L:=["Var 2","Var 3","Var 6"]:

S:=[["Var 2","Var 3"], ["Var 6"] ];

                                                            S := [["Var 2", "Var 3"], ["Var 6"]]

> Parametric(T,L,S);

  <p[0, 0, 0] - t[1, 2, 0, 0] t[3, 0],

        p[0, 0, 1] - t[1, 2, 0, 0] t[3, 1],

        p[0, 1, 0] - t[1, 2, 0, 1] t[3, 0],

        p[0, 1, 1] - t[1, 2, 0, 1] t[3, 1],

        p[1, 0, 0] - t[1, 2, 1, 0] t[3, 0],

        p[1, 0, 1] - t[1, 2, 1, 0] t[3, 1],

        p[1, 1, 0] - t[1, 2, 1, 1] t[3, 0],

        p[1, 1, 1] - t[1, 2, 1, 1] t[3, 1]>

Equatn(table, list, sigma);

table -  the list of lists containing all the data.

list -   the list ["var 1", ... , "var n"] with the names of the variables involved in the independence model.

sigma-  the list of lists  [ ["var 1" , ... , "var h"] , ... , ["var k" , ... , "var n"] ] containing the groups of variables of which the user wants to study the independence.

The Equatn command gives the equation of the independence model, using the EliminationIdeal command on the parametric equation of the model built with the Parametric command.

The independence model is expressed by the parameters 'list' and 'sigma'.

For example, if we want to study the independence of two variables from a third one, the parameters would be:

list:=["var1" , "var2" , "var3"];  sigma:=[ ["var1", "var2"] , ["var3"] ];.

The parameter 'table' can be obtained from an Excel file using the command 'TableT'. If  the table is written directly in Maple by the user, please read the TableT instructions to write it in the correct form.

T:=TableT("exemfile.xls"):

L:=["Var 2","Var 3","Var 6"]:

S:=[["Var 2","Var 3"], ["Var 6"] ]:

Equatn(T,L,S);

<p[0,1,0]*p[0,0,1]-p[0,1,1]*p[0,0,0], p[0,1,1]*p[1,0,0]-p[1,0,1]*p[0,1,0], p[1,0,0]*p[0,0,1]-p[1,0,1]*p[0,0,0], p[1,1,0]*p[0,0,1]-p[1,1,1]*p[0,0,0], p[1,1,0]*p[0,1,1]-p[1,1,1]*p[0,1,0], p[1,1,0]*p[1,0,1]-p[1,1,1]*p[1,0,0]>

ModelMatrix(table, list, sigma);

table -  the list of lists containing all the data.

list -  the list ["var 1", ... , "var n"] with the names of the variables involved in the independence model.

sigma-  the list of lists  [ ["var 1" , ... , "var h"] , ... , ["var k" , ... , "var n"] ] containing the groups of variables of which the user wants to study the indipendence.

The ModelMatrix command builds the matrix of the independence model considered.

The independence model is expressed by the parameters list and sigma.

For example, if we want to study the independence of two variables from a third one, the parameters would be:

list:=["var1" , "var2" , "var3"];  sigma:=[ ["var1", "var2"] , ["var3"] ];.

The parameter 'table' can be obtained from an Excel file using the command 'TableT'. If  the table is written directly in Maple from the user, please read the TableT instructions to write it in the correct form.

T:=TableT("exemfile.xls"):

L:=["Var 2","Var 3","Var 6"]:

S:=[["Var 2","Var 3"], ["Var 6"] ]:

ModelMatrix(T,L,S);

                [1    1    0    0    0    0    0    0]

                 [0    0    1    1    0    0    0    0]

                [0    0    0    0    1    1    0    0]

                [0    0    0    0    0    0    1    1]

                [1    0    1    0    1    0    1    0]

                [0    1    0    1    0    1    0    1]

MaxLikeEst(table,list,sigma);

table -  the list of lists containing all the data.

list -  the list ["var 1", ... , "var n"] with the names of the variables involved in the independence model.

sigma-the list of lists  [ ["var 1" , ... , "var h"] , ... , ["var k" , ... , "var n"] ] containing the groups of variables of which the user wants to study the independence.

The MaxLikeEst command computes the Maximum Likelihood Estimation of the indipendence model considered.

The independence model is expressed by the parameters 'list' and 'sigma'.

For example, if we want to study the independence of two variables from a third one, the parameters would be:

list:=["var1" , "var2" , "var3"];  sigma:=[ ["var1", "var2"] , ["var3"] ];.

The parameter 'table' can be obtained from an Excel file using the command 'TableT'. If  the table is written directly in Maple by the user, please read the TableT instructions to write it in the correct form.

T:=TableT("exemfile.xls"):

L:=["Var 2","Var 3","Var 6"]:

S:=[["Var 2","Var 3"], ["Var 6"] ]:

MaxLikeEst(T,L,S);

{p[0,0,0] = 36/361, p[0,0,1] = 40/361, p[0,1,0] = 45/361, p[0,1,1] = 50/361, p[1,0,0] = 45/361, p[1,0,1] = 50/361, p[1,1,0] = 45/361, p[1,1,1] = 50/361}

PearsonCoeff(p,K);

p - maximum likelihood extimation, expressed as a list

K - the list of frequencies

The PearsonCoeff command computes the Pearson coefficient with vector of frequencies K and MLE p.

p:=[36/361, 40/361, 45/361,  50/361,  45/361,  50/361,  45/361,  50/361}]:

k:=[3,1,2,3,2,3,2,3]:

PearsonCoeff(p,k);

                                                            931/600

DiaconisSturmfels(table,list,sigma, n);

table -  the list of lists containing all the data.

list -  the list ["var 1", ... , "var n"] with the names of the variables involved in the independence model.

sigma -  the list of lists  [ ["var 1" , ... , "var h"] , ... , ["var k" , ... , "var n"] ] containing the groups of variables of which the user wants to study the independence.

n - the number of iterations

This command applies the Diaconis-Sturmels algorithm on the independence model considered to compute an estimation of the p-value, called the Monte Carlo

p-value.

The indipendence model is expressed by the parameters 'list' and 'sigma'.

For example, if we want to study the independence of two variables from a third one, the parameters would be:

list:=["var1" , "var2" , "var3"];  sigma:=[ ["var1", "var2"] , ["var3"] ];.

The parameter 'table' can be obtained from an Excel file using the command 'TableT'. If  the table is written directly in Maple from the user, please read the TableT instructions to write it in the correct form

T:=TableT("exemfile.xls"):

L:=["Var 2","Var 3","Var 6"]:

S:=[["Var 2","Var 3"], ["Var 6"] ]:

DiaconisSturmfels(T,L,S,10000);

                             0.8096000000