Census Reporter Inputs Window

Generalities
The Census Reporter Inputs window (Analysis > Circuit Census (CTRL+H) ) enables to set and operate a circuit census on your dataset. It presents a number of parameters, which can be used depending on the analysis needs.

Pattern Field
The Pattern field is a fundamental tool, which enables you to define the type of circuits that you wish to count. It allows you to define the type of census desired : consanguine marriages, two-groups and three-groups relinking. It can be used, for circuits counting, by resorting to two input methods.

• The first way to use the Pattern field is to specify the maximal dimensions of the matrimonial circuits to be searched for.
  Matrimonial Circuits have two dimensions : their width (or order) and their maximal canonic degree of consanguine relations (or depth). The first number to type into the Pattern field indicates the maximal canonic degree of circuits with width 1 (i.e. incorporating 1 marriage arc, corresponding to consanguine unions) ; the second number indicates the maximal canonic degree of circuits with width 2 (i.e. incorporating 2 marriage arcs, corresponding to two-groups relinkings), the third number indicates the maximal canonic degree of circuits with width 3 (i.e. incorporating 3 marriage arcs, corresponding to three-group relinkings).
  For instance, the code 3 2 1 sets the horizon of matrimonial circuit search to blood marriages between 2nd cousins (degree 3), marriage redoublings between pairs of 1st cousins (degree 2) and marriage retriplings between pairs of siblings (degree 1). All circuits/relations of lower dimensions (for instance, blood marriages between first cousins or marriage redoublings between pairs of siblings) are included in the search.
  
  
• The second way to use the Pattern field is to enter a structural schema expressed in positional notation (i.e. XX(X)XX will find all circuits corresponding to marriages between cousins). Note that, as a rule, a structure formula is read by Puck in a socio-centered manner. That is, the formula X(H)HX and XH(H)X designate one and the same type of relation. This is important if the census is run on a subcorpus, where ego may be in but alter may not. Without further indication, a structure formula limits search to circuits/relations that exactly fit this formula (unlike the first method which only sets an upper limit). We can, however, include all circuits/relations which lie within the limits of the formula by letting it precede the character “<”. For instance, the formula “<XXX(X)XX” limits the search to all blood marriage circuits within the limits of the 5th civil degree (including marriages between first cousins, between uncles and nieces etc.). Juxtaposition of several structure formula is interpreted as a combination by logical “or”. For instance, the formula X.X(X)X XX(X)XX limits circuit search to marriages between siblings in-law or 1st cousins.

After setting the Pattern field, a matrimonial census can then be refined according to specific criteria, i.e. : Filiation, Symmetry, Sibling, Circuit and Restriction types.

Filiation Type
The Filiation Type checkbox enables to choose the type of permitted consanguinity relations to be included in the query.
It can be set in four possible ways :

• Cognatic : all consanguinity relations are permitted ;
  
• Agnatic : only agnatic relations are permitted (unilinear census) ;
  
  
• Uterine : only uterine relations are permitted (unilinear census) ;
  
• Bilateral : only bilateral relations are permitted.
  

Symmetry Type
The Symmetry Type checkbox enables to decide on the relations permutability between ego and alter. For example, if kinship chains between co-residents are searched, the option “symmetry” has to be activated, for co-residence being a symmetric relation. Accordingly, the chains “father-son” and “son-father” will be counted as one single category. By contrast, if kinship chains between persons and their heirs are searched, the option “symmetry” has to be deactivated, for inheritance being an asymmetric relation. Accordingly, the chains “father-son” and “son-father” will be counted as different categories.

Note : the symmetry type choice is only relevant for a non-matrimonial circuit census. If matrimonial circuits or open kinship chains are searched, ego and alter are always considered as permutable (in the first case, male or female ego will be chosen according to the chosen option, in the second case, there is no criterion for the selection of ego or alter).

Sibling Type
The Sibling Type checkbox enables to choose the type of sibling differentiation. This can be set in three possible ways :

• 2 (None) : no siblings assimilated. Only paternal and maternal siblings are distinguished, full siblings are counted twice (once as paternal and once as maternal siblings). This method is recommended when half-sibling relations are frequent (e.g. because of high rates of polygamy) the agnatic or uterine relationship is more important than the sibling relationship as such.
  
  
• 3 (Full) : full siblings assimilated. True paternal and maternal half-siblings are distinguished from full siblings. This method provides the maximum of information.
  
  
• 1 (All ) : all siblings assimilated. Full and half siblings are not distinguished. This method is recommended when half sibling relations rarely occur or do not matter for marriage rules.

Circuit Type
The Circuit Types frame includes the following options :

• Circuit : counts matrimonial circuits.
  
  
• Ring : does not consider circuits/relations that completely include shorter ones (matrimonial rings and not all matrimonial circuits).
  
  
• Minor : does not consider circuits/relations that intersect with shorter and narrower ones (minor matrimonial rings and not all matrimonial circuits).
  
  
• Minimal (Minimal rings only) : does not consider circuits/relations that intersect with shorter ones (minimal matrimonial rings and not all matrimonial circuits)

Restriction Type
The Restriction Types frame options are :

• All : all married individuals (matrimonial circuit pivots) must belong to the chosen cluster.
  
  
• Ego : ego (according to a chosen kinship schema) must belong to the chosen cluster (presupposes a search expressed by formula).
  
  
• Last married : the last married individual must belong to the chosen cluster (presupposes marriage dates, for the moment they were still treated as individual properties). With closing relation, it is possible to choose different types of censuses (matrimonial, relational, absence of closing relations) from endogenous or exogenous properties (occupation, residence etc.), extending the search criteria and producing diagrams.

***GAP Other Settings

• The Details and Diagrams frame allows [...] The Label column enables to choose [...] The Report and Diagram check-boxes allow to [...]
  
  
• The Couples only check-box [...]
  
  
• The Mark Individuals check-box allows adding the binary property of being in a circuit of a given type to each individual who forms a pivot of a circuit. The label of the property is the circuit type in standard notation, preceded by "CENSUS" (see the Individual Property Codes). The property includes indication of Alter and appears in the Additional Data frame. 
  Partitioning the corpus according to such a property permits to extract/expand the sub-corpus of all individuals that are part of a circuit of the given type.
  Using this property for redefining spouses in order to effect a second relational or matrimonial census permits a complex matrimonial or relational census (multiple kinship relations or intersecting matrimonial circuits).
  
  
• The Circuits as Relations check-box [...]
  
  
• The Cross-sex chains only check-box [...]
  
  
• The List out-of-circuits pairs check-box [...]
  
  
• The List all perspectives check-box [...]

***Filter
The Filter field allows excluding from a circuit census a relation type. You can define the relation to be filtered by typing it in positional notation.

***Open Chains Frequencies and Closure Rate
A Relational Census can be used both in order to count non-matrimonial relations and, which is more important for a kinship network structural analysis, to evaluate some of the dataset biases. For example, if in a kinship network the number of cross patrilateral cousins is much greater than the number of cross matrilateral ones, marriages between the former will automatically result more frequent. Thus, the prominence of a given marriage type does not necessarily indicate a social preference for that type of marriage. It can merely result from the higher frequency of that specific relation (not "closed" by a marriage tie) compared to others. Thus, to understand high frequencies of given matrimonial circuits as a direct sign of a social preference can reveal itself misleading. 
The closure rate (Hamberger & Daillant, 2008, p. 27-28) is an indicator that has been conceived to prevent such mistakes. As it appears in the snapshot showed below, a calculation of the Closure Rate can be obtained by selecting, in the PUCK Census Reporter Inputs window, the Open Chains Frequencies check-box. Then, on the Results table, for each type of matrimonial circuit will both appear : the total Open Chains number and its Closure Rate.

Matrimonial networks for Pajek
The frame Circuit to include in Pajek format allows generating matrimonial networks to be analyzed in Pajek.

It has to be set before launching a census ad it includes several possibilities :

• Circuits as network : exports all matrimonial circuits found by the census as separate networks (with nominal indication of individuals as vertex labels), as well as a partition to distinguish vertices that occupy spouse positions in the circuit.
  
  
• Circuit induced network : produces the matrimonial network corresponding to the matrimonial census (that is a network made up only of the links that form part of some matrimonial circuit), as well as a partition to distinguish vertices that occupy spouse positions in the matrimonial network.
  
  
• Circuit induced frame network : (consanguine chains reduced to lines) produces the matrimonial network frame corresponding to the matrimonial census, embedded in the total kinship network in which marriages are coded according to the circuit(s) they are part of. This may provide a synthetic representation in which certain connective features of the matrimonial network can be identified.
  
  
• Circuit intersection network : produces the circuit intersection network corresponding to the matrimonial census, as well as the circuit intersection matrix (Hamberger & Daillant, 2008, p. 22‑24).

***Relational to Complex Matrimonial Census
If the matrimonial circuit census counts the matrimonial circuits in a kinship network, a non-matrimonial circuit census counts relational circuits, which are kinship chains "closed" by a previously defined relation (for instance, co-residence, friendship, etc.). The Closing relation frame enables to run such a census, by selecting the wanted relation.
As shown in the example above, setting the Closing Relation to "Open" and selecting the Couples only checkbox leads to a census of open chains concerning married people.

A more complex relational or matrimonial census can be effectuated by combining two censuses, using the results of the first (stored as relational properties by the Mark Individuals function) in order to redefine spouses, and running the second census on the thus transformed corpus.
In this manner, one can search for MBD marriages that are at the same time ZD marriages, bilateral cross cousins, and so on.
Such a complex census is a useful analytical complement to the inspection of the circuit intersection network.
***CORR? Instead of generating relational data from a preliminary relational or matrimonial census, they can also be directly read from a file, for instance a list of ego-alter-pairs (in the form of a two-column text file). For the precise method see the entry Relational properties from text files.

Mixed Matrimonial and Connubial Circuits
***CORR***
Puck allows regrouping individuals according to a certain property (chosen from a drop-down menu by double clicking on the checkbox label) and effectuate a census of :

• Mixed Matrimonial Circuits containing the relation “belonging to the same cluster”. Puck distinguishes for the moment 9 types of mixed matrimonial circuits, according as the H, HF, or HM belongs to the same cluster as W, WF or WM.
  
  
• Connubial Circuits : Puck distinguishes endogamous circuits (1 group), redoubling or exchange circuits (2 groups, arrows pointing in the same or in inverse directions) and cycle circuits (3 groups, arrows consistently directed). For each circuit, the census lists the number of connubial circuits, the number of distinct cycles that may be formed from the marriages that constitute the connubial circuit, the weight of the circuit (the geometric mean of marriages joining two groups in the circuit) and the probability of the circuit, given the relative numbers of potential spouses in the constitutive groups.
  

***GAP Reshuffling
The Launch with Reshuffling button allows [...]

Circuit Census : Results and Tables

After launching a circuit census, PUCK produces a report in which are indicated : the precise number and type of the searched circuits, as well as their classification (as individuals and couples). Each report can be saved in .txt or .xls formats, by clicking on the "Save" button placed in the bottom right-hand corner.

Report Tabs
Each report is subdivided in five tabs :

• Census : indicates the total number of circuits and the maximum height (the canonic degree), the number of different circuits, the number of individuals and couples involved, in absolute numbers and as percentages, both in total and on the circuits concerned.
  
  
• Circuits : lists, for each type of circuit/relation (indicated in standard notation), all relations found in the corpus, with nominal indication of their pivots (and their relations: “=” for marriage, “-” for consanguinity) and the complete chain in positional notation (individuals being indicated by their identity numbers).
  
  
• Couples : lists, for each couple or pair of relatives concerned by the census, all the circuits/relations that link them, both in standard notation of the type and in positional notation of the complete chain (individuals being indicated by their identity numbers).
  
  
• Sortable list : List all relations found in the census, with the index, standard and positional notation of the relation/ring type, nominal indication of their pivots and their relations (“=” for marriage, “-” for consanguinity) and the complete chain in positional notation (individuals being indicated by their identity numbers).
  
  
• ***Diagrams : currently, this function is not implemented.