binary data

Examples of binary data in the following topics:

• Intorduction to qualitative analysis

  • That is, either an actor was, or wasn't present, and our incidence matrix is binary.
  • This is because the various dimensional methods operate on similarity/distance matrices, and measures like correlations (as used in two-mode factor analysis) can be misleading with binary data.
  • Even correspondence analysis, which is more friendly to binary data, can be troublesome when data are sparse.
  • In principle, one could fit any sort of block model to actor-by-event incidence data.
  • Alternative block models, of course, could be fit to incidence data using more general block-modeling algorithms.

• Introduction to finding equivalence Sets

  • With binary data, numerical algorithms are used to search for classes of actors that satisfy the mathematical definitions of automorphic equivalence.
  • One approach to binary data, "all permutations," (Network>Roles & Positions>Automorphic>All Permutations) literally compares every possible swapping of nodes to find isomorphic graphs.
  • For larger data sets, and where we are willing to entertain the idea that two sub-structures can be "almost" equivalent, optimization is a very useful method.
  • When we have measures of the strength, cost, or probability of relations among nodes (i.e. valued data), exact automorphic equivalence is far less likely.
  • This method can also be applied to binary data by first turning binary adjacency into some measure of graph distance (usually, geodesic distance).

• Categorical REGE for directed binary data (Wasserman-Faust directed data)

  • Our example will be of a binary graph; the algorithm, however, can also deal with multi-valued nominal data (e.g. "1" = friend, "2" = kin, "3" = co-worker, etc.).
  • Once a regular equivalence blocking has been achieved, it is usually a good idea to produce a permuted and blocked version of the original data so that you can see the tie profiles of each of the classes.
  • One way to do this is to save the permutation vector from Network>Roles & Positions>Maximal Regular>CATREGE, and use it to permute the original data (Data>Permute).

• Two-mode correspondence analysis

  • For binary data, the use of factor analysis and SVD is not recommended.
  • When the connections of actors to events is measured at the binary level (which is very often the case in network analysis) correlations may seriously understate covariance and make patterns difficult to discern.
  • As an alternative for binary actor-by-event scaling, the method of correspondence analysis (Tools>2-Mode Scaling>Correspondence) can be used.
  • Correspondence analysis (rather like Latent Class Analysis) operates on multi-variate binary cross-tabulations, and its distributional assumptions are better suited to binary data.
  • Since these data do not reflect partisanship, only participation, we would not expect the findings to parallel those discussed in the sections above.

• Univariate descriptive statistics

  • Figure 18.1 lists these data.
  • These particular data happen to be asymmetric and binary.
  • If data are symmetric (i.e.
  • The sums of squared deviations from the mean, variance, and standard deviation are computed -- but are more meaningful for valued than binary data.
  • With valued data, measures of variability may be more informative than they are with binary data (since the variability of a binary variable is strictly a function of its mean).

• Categorical REGE for geodesic distances (Padgett's marriage data)

  • The Padgett data on marriage alliances among leading Florentine families are of low to moderate density.
  • The data are binary, and not directed.
  • Since the data are highly connected and geodesic distances are short, we are not able to discriminate highly distinctive regular classes in these data.
  • The use of REGE with undirected data, even substituting geodesic distances for binary values, can produce rather unexpected results.
  • But, in my opinion, it should be used cautiously, if at all, with undirected data.

• Data and Information

  • Data consists of nothing but facts, which can be manipulated to make it useful; the analytical process turns the data into information.
  • Binary files (readable by a computer but not a human) are sometimes called "data" and are distinguishable from human-readable data, referred to as "text" .
  • Once data is in digital format, various procedures can be applied on the data to get useful information.
  • Data processing may involve various processes, including:
  • Data processing may or may not be distinguishable from data conversion, which involves changing data into another format, and does not involve any data manipulation.

• Multiplex data basics

  • Multi-plex data are data that describe multiple relations among the same set of actors.
  • The measures of the relations can be directed or not; and the relations can be recorded as binary, multi-valued nominal, or valued (ordinal or interval).
  • Figure 16.1 shows the output of Data>Display for the Knoke social welfare organizations data set, which contains information on two (binary, directed) relations: information exchange (KNOKI), and money exchange (KNOKM).
  • Some matrices may be symmetric and others not; some may be binary, and others valued.
  • A number of the tools that we will discuss shortly, however, will require that the data in the multiple matrices be of the same type (symmetric/asymmetric, binary/valued).

• Introduction to kinds of graphs

  • Figure 3.2 is an example of a binary (as opposed to a signed or ordinal or valued) and directed (as opposed to a co-occurrence or co-presence or bonded-tie) graph.
  • Figure 3.3 is an example of a "co-occurrence" or "co-presence" or "bonded-tie" graph that is binary and undirected (or simple).
  • Figure 3.4 is an example of one method of representing multiplex relational data with a single graph.

• Levels of measurement: Binary, signed, and valued graphs

  • If we asked each respondent "is this person a close friend or not," we are asking for a binary choice: each person is or is not chosen by each interviewee.
  • When our data are collected this way, we can graph them simply: an arrow represents a choice that was made, no arrow represents the absence of a choice.
  • This kind of data is called "signed" data.
  • The graph with signed data uses a + on the arrow to indicate a positive choice, a - to indicate a negative choice, and no arrow to indicate neutral or indifferent.
  • Yet another approach would have been to ask: "rank the three people on this list in order of who you like most, next most, and least. " This would give us "rank order" or "ordinal" data describing the strength of each friendship choice.