+------------ User's Manual ------------+
| STATISTICAL |
| ENTAILMENT ANALYSIS 2.0 |
| SEA.EXE |
+=======================================+
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| M U L T I - D I M E N S I O N A L |
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| G U T T M A N S C A L I N G |
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+===== 8888 La Jolla Scenic Dr. N. =====+
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TABLE OF CONTENTS page
1. Introduction: 1
.1 Purpose of MGS 1
.2 Use of Entailments 2
.3 Procedures 3
2. Guttman Scales 4
3. Transitivity 5
.1 Weak Form: Partial Correlation 6
.2 Strong Form: Cumulative Exceptions 7
4. Input Data File 8
5. Running the Program 10
6. Output 11
.1 Step 1: Table 1 Cross Tabulations 11
.1.1 Exclusions and Coexhaustives 13
.1.2 Table 1 for Negative Entailments 14
.1.3 Contrapositives 14
.1.4 Equivalences 15
.2 Step 2: Table 2 Randomization 16
.3 Step 3: Table 3 Expected & Actual 17
.4 Step 4: Table 4 Signal Detection 18
.5 Step 5: Table 5 Transitivity 20
.6 Step 6: Entailment Chains by Level 23
7. Drawing the Entailment Hierarchy 24
8. Advanced Options 26
ENDNOTES 29
9. References to MGS and Precursors 30
10.References to Guttman Scaling 31
Software License 32
MULTIDIMENSIONAL GUTTMAN SCALING
(c) 1986 Douglas R. White
1. Introduction.
1.1 Purpose of MGS
MGS methods represent a major revision of
conventional Guttman Scaling techniques
(section 10). Questions of scale errors
(section 2) and use of errors to measure
scalability of variables (section 10) are
treated in the context of exceptions to
the entailment relationships between
variables ("If X is present then Y is
present") which constitute the scale.
The transitivity of entailments (If X
then Y and If Y then Z imply If X then Z)
becomes a crucial scaling criterion.
Using MGS, as many as 50 dichotomous
variables can be examined to define a
network of transitive entailments.
Unlike earlier approaches to multiple
Guttman scaling (Lingoes; Mokken), MGS
gives an integral, relational, and truly
multidimensional approach to the implica-
tional scaling of dichotomous items.
- 1 -
1.2 Use of Entailments
MGS procedures provide a statistically
optimized description of the structure of
dichotomously coded data by identifying
entailment relationships. An entailment
is one of four types of implicational
relationships such as "if X is present
then Y is present", with (i) a
percentage Pxy of exceptions to the
implication, and (ii) statistical
relevance as measured by the strength of
association in the cross-tabulation of
the variables.
Entailments between two positively
correlated variables X and Y are written
(see endnote 1) as:
1. X <-- Y (X entails Y), with Pxy %
exceptions; and its converse,
2. Y <-- X, with Pyx % exceptions.
Two other types of entailment apply where
the variables are negatively correlated:
3. X <-- -Y (X entails not-Y), with
Px-y % exceptions; and its converse,
4. -Y <-- X, with P-yx % exceptions.
- 2 -
1.3 Procedures
Special features of the MGS method and
program are explained in this manual.
The manual is organized around a sample
MGS run which uses the data file depicted
in Table 0, Section 2. For learning
purposes, experiment by running MGS on
modifications of this datafile.
Although the example shows a unidimen-
sional scale, MGS is not limited to data
where a unidimensional scale is
hypothesized.
The MGS analysis involves a three phase
process where you prepare a data file,
run MGS, and draw the entailment
hierarchies from the output.
Begin by reading sections 2 and 3 to
understand the procedures used in the
program.
- 3 -
2. Guttman Scales.
A cumulative scalogram or Guttman
scale is described by a directed chain of
entailments such as W <-- X <-- Y <-- Z.
This pattern of relationships is exempli-
fied in the following coded dichotomous
data, where 1 indicates presence and 0
absence, with 9 for missing data:
TABLE 0
W X Y Z Observation
| 1 1 1 1 1
|__1__ 9 1 1 2
0 | 1 0 1 3
0 |__1__ 1 1 4
0 0 |__1__ 1 5
0 0 0 | 1 6
9 0 0 |__1__ 7
0 0 0 0 | 8
In this scale, observations 1, 4, 5, 6,
and 8 are "pure" scale types which fit
the expected scale pattern perfectly.
Observations 2 and 7 are "consistent"
scale types which fit the pattern but
contain missing data. Observation 3, on
- 4 -
the other hand, contains a scale error:
the Guttman scale pattern as well as the
entailment X <-- Y predicts that if X is
present then Y will be present, or if Y
is absent then X will be absent. There
are six constituent entailments in this
scale with the following percentages of
exceptions:
W <-- X 0 % exceptions (Pwx)
W <-- Y 0 % exceptions (Pwy)
W <-- Z 0 % exceptions (Pwz)
X <-- Y 14.3 % exceptions (Pxy)
X <-- Z 0 % exceptions (Pxz)
Y <-- Z 0 % exceptions (Pyz)
3. Transitivity.
MGS builds on the assumption that
a major criterion for a Guttman scale is
the transitivity of directed chains of
entailment such as described above. When
X entails Y, or X <-- Y, and Y entails Z,
or Y <-- Z, we infer by transitivity that
X entails Z. There are two kinds of
measure of transitivity, weak and strong.
The weaker is determined by the measure
of partial correlation. The stronger is
- 5 -
determined by cumulativity of exceptions:
in a chain X <-- Y <-- Z: whether the
exception rate Pxz equals or exceeds the
sum of Pxy and Pyz, their maximum, their
average, or their minimum.
3.1 Weak Form: Partial Correlation
In directed entailment chains X <- Y <- Z
a negative partial correlation between X
and Z controlling for Y (the intervening
variable) is evidence of Guttman scale
intransitivity. In a perfect Guttman
scale (all pure scale types; no errors in
constituent entailments) all such partial
correlations are necessarily zero. Zero
or positive partials, with imperfect
scales, are evidence of scalability or
fit to the scale pattern. This provides
the weakest criterion where transitivity
is considered to be satisfied:
Rule 1. Partial correlations are zero,
positive, or very close to zero if
negative with missing data.
A stronger criterion is:
- 6 -
Rule 2. Partial correlations are zero or
positive.
Neither criterion distinguishes the
directionality of the entailments for
patterns such as Table 0. Here, for
example, both W <- X <- Y <- Z and its
converse Z <- Y <- X <- W exemplify rule
2 of non-negative partials.
3.2 Strong Form: Cumulative Exceptions
For an entailment chain X <- Y <- Z, the
% exceptions Pxz, Pxy and Pyz are used to
evaluate strong forms of transitivity.
Unless missing data are present, it is
necessarily true that Pxz < Pxy + Pyz.
The following three rules, however,
provide transitivity criteria of
increasing strength:
Rule 3. Pxz < maximum (Pxy, Pxz)
Rule 4. Pxz < average (Pxy, Pxz)
Rule 5. Pxz < minimum (Pxy, Pxz)
- 7 -
The stronger rules of transitivity may
distinguish directionality of entailment.
For example, the entailments originally
described for Table 0 satisfy rules 1
through 5, while the converse entailment
chain (with arrows reversed) satisfies
rules 1, 2, and 3 (see endnote 2), but
not 4 or 5. (Recall that in general
Pxy /= Pyx.)
4. Input Data File.
MGS is a batch program. Data are
read from a text file. The data in Table
0 are contained the following file:
4 8 5
TEST DATA TITLE
(4I2)
1 1 1 1
1 9 1 1
0 1 0 1
0 1 1 1
0 0 1 1
0 0 0 1
9 0 0 1
0 0 0 0
- 8 -
An MGS INPUT DATA FILE consists of a
parameter line, a title line, a format
line, and data lines as illustrated.
The first line of the input data file
gives the number of variables (above: 4)
in columns 2-3. The number of
observations (e.g. 8) in columns 4-6 is
optional. If it is not given, the
program will look for an end-of-file
marker and ask you to reenter the
name of the input data file. The
transitivity parameter in column 11 is
also optional. If not specified, it is
set by default to 4 (section 3.2: rule
4).
The second line indicates that TEST DATA
is the title of the dataset. Leave the
first column of this line blank.
The third line gives the FORTRAN integer
format for reading the data which follows
it (leave first column blank). Thus,
format (4I2) will read four two-column
variables, and looks for data in columns
2,4,6,8.
- 9 -
There are 16 other optional parameters
with defaults described in the advanced
options section (8). You do not need
these options to get started running MGS.
5. Running the Program.
The program is started by entering:
>MGS
You will then be asked to specify CON: if
you want output to appear on the console.
Press Control-PrtSc for console output
to appear on your printer. If you want
to save the output as a datafile, give
a desired filename, and press the ENTER
key. If you do so, be prepared to wait
until the program finishes without seeing
anything on your screen. No output
datafiles will be saved unless the
execution is finished.
The program will ask for the name of the
input data file, followed by the ENTER
key, to begin execution.
- 10 -
6. Output.
MGS output to the screen includes
the logo, copyright statements, the num-
ber of variables, title, format, list of
parameters (section 8 default settings),
various instructions, item frequencies,
and the summary signal detection table 4
(section 6.4). Next are listed variables
which have identical codes, or are always
coded present or always coded absent.
Finally come the transitive entailments
in Table 5 (section 6.5), and entail-
ments chains at various levels of
exceptions (section 6.6). TABLE1 (Cross-
Tabulations), TABLE2 (Sample Random
Data), and TABLE3 (Actual vs. Expected
Frequencies of Entailments of each type,
at various strength of correlation and
levels of exceptions), are discussed in
sections 6.1, 6.2, and 6.3, and will
appear in the default disk drive.
6.1 Step 1: TABLE1 Cross-Tabulations
The first step in analysis is cross-
tabulation of all pairs of variables.
- 11 -
Each pair of variables appears in an
output file, TABLE1, which will appear on
the default disk drive.
Table 1 X<-Y Y<-X
VARS. RELE- EXCEP- EXCEP- 2x2 Tables
X Y VANCE TIONS TIONS A B C D
==1== ==2== ===3=== ===4=== = = = =
1 2 .447 .000 S .333 W 1 0 2 3
1 3 .548 .000 S .286 W 2 0 2 3
1 4 .258 .000 S .571 W 2 0 4 1
2 3 .417 .143 S .143 S 2 1 1 3
2 4 .354 .000 S .429 W 3 0 3 1
3 4 .378 .000 S .375 W 4 0 3 1
The two columns under ==1== in Table 1
are the pairs of variables. Under ==2==
are the correlation coefficients (Pearson
tetrachloric r). Under ===3=== is Pxy (%
exceptions) for the entailment X <- Y.
This entailment is classified as S
(strong) if the % exceptions Pxy are less
than or equal to Pyx, the % exceptions of
the converse entailment Y <- X.
Otherwise, the entailment is classified
as W (weak). Under ==4== is Pyx and the
classification of the converse entailment
as S or W. The last four columns are
- 12 -
labelled for the cells in the 2x2 table:
Y + Y -
+----+----+
X + | A | B |
2x2 Table +----+----+
X - | C | D |
+----+----+
Note that Pxy = B/N and Pyx = C/N, where
N =A+B+C+D is the number of observations.
6.1.1 Exclusions and Coexhaustives
In the example in Table 0, all of the
correlations are positive and exceptions
to the entailments occur only in cells B
or C in the above table. This is not
necessarily the case, and the other two
types of entailments are now discussed
to give full generality to MGS:
i) Exclusion is an entailment of the
form X <-- -Y (section 1.2), where the
exceptions Px-y occur in cell A of the
2x2 table.
- 13 -
ii) Coexhaustion is an entailment
of form -X <-- Y, where the exceptions
P-xy occur in cell D of the 2x2 table.
6.1.2 TABLE1 for Negative Entailments
Negative correlations between variables
will also appear in TABLE 1. Percentage
exceptions for exclusions will be in
column ===3=== followed by the letter E.
% exceptions for coexhaustions will be in
column ===4=== followed by the letter C.
6.1.3 Contrapositives
Entailment analysis (the MGS program)
encompasses multi-dimensional Guttman
scaling, but has by virtue of the two
types of negative entailments a more
general applicability to describing set-
subset relationships (Boolean algebra) or
first-order predicate logic. In logic,
the contrapositive of an entailment "If X
then Y" is the equivalent entailment made
by reversing the order and signs of the
variables: "If not Y then not X." The
- 14 -
four types of directed entailments, with
equivalent contrapositives, correspond to
the four error cells of the 2x2 table:
A. X <-- -Y = Y <-- -X
B. X <-- Y = -Y <-- -X
C. Y <-- X = -X <-- -Y
D. -X <-- Y = -Y <-- X
6.1.4 Equivalences
An equivalence between two variables is
represented by double arrows, X <-> Y,
and occurs when cells B and C of the
2x2 table are empty (perfect
correlation). A negative equivalence,
-X <-> Y or X <-> -Y, occurs when cells
A and D of the 2x2 table are empty
(perfect negative correlation). When
either of these two conditions occurs
with no missing data, a set of perfectly
correlated variables is identified by the
program, and all but the first variable
in the set are dropped from subsequent
analysis since all equivalents have
identical entailments.
- 15 -
6.2 Step 2: TABLE2 Randomization
To determine the significance of 2x2
tables MGS does not rely on tests for
individual tables but on comparable 2x2
classifications of randomized variables
having the same marginal frequencies as
the actual data. In this step, each
variable in the analysis is randomized
(see advanced options) and step 1 is
repeated for the randomized data. Sample
random data are saved in file TABLE2. In
the example above (data: Table 0), a
possible result of randomization is:
TABLE2
0 0 1 1
1 9 1 1
1 1 0 0
0 1 1 1
0 0 1 1
0 1 0 1
9 0 0 1
0 0 0 1
An analysis of random data comparable to
that of the actual data allows MGS to
determine whether the observed entailment
results are likely to be due to chance.
- 16 -
Low frequency variables, for example, are
likely to entail high frequency ones by
chance alone.
6.3 Step 3/Table 3 Expected & Actual
Randomization and the analysis of random
data is usually repeated more than once
(default: 2) and averaged to obtain an
baseline for expected frequencies of
entailments of various sorts and levels.
Sample results are shown in Table 3,
where the actual and expected frequencies
of each of the four types of entailment
(strong inclusion, weak inclusion,
exclusion, and exclusion). are classified
as to (1) degree of correlation and (2)
percent exceptions.
TABLE 3 ACTUAL:RANDOM
STRONG INCLUSION FREQUENCIES
CLASSIFIED BY STRENGTHS OF CORRELATION:
and >.5 >.4 >.3 >.2 >.1
EXCEPTIONS
=========================================
.000 1:0 1:.5 2:1 1:0 0:0
.125 0:0 0:0 0:0 0:0 0:0
.250 0:0 2:0 0:0 0:0 0:0
- 17 -
As seen in this portion of table 3, two
entailments occurred with zero exceptions
and a correlation of above .4 while only
one occurred in two random datasets;
four occurred above .3, with 1.5 by
chance; five occurred above .2 with 1.5
by chance. With one exception (% = .143)
two entailments occurred above .4, with
none by chance. In all, seven entailments
occurred with 1 or fewer exceptions above
a .2 correlation, while 1.5 occurred by
chance. The ratio of actual to random
entailments at this level is 4.67:1.
6.4 Step 4: Table 4 Signal Detection
Signal detection methods are applied to
the data in Table 3 to pick the optimal
cutoff levels for entailments of each
type. First, a cutoff is determined at
each level of exceptions for the lowest
correlation at which the cumulative
number of actual entailments exceeds the
cumulative number expected for all
entailments at this level or stronger (to
alter the actual-to-expected cutoff ratio
see section 8 col. 32-34). For Table 3
- 18 -
COMPLETE EQUIVALENCIES:
this occurs at .10 in row 1 and 2. These
cutoffs are given in the first of two
columns on Table 4. A sample appears
below as it will on the console:
TABLE 4: SIGNAL DETECTION
(1) CUTPOINTS (2) SIGNAL-TO-NOISE RATIO
STRONG WEAK
INCLUSIONS INCLUSIONS
(1) (2) (1) (2)
E < .000 > .10 3.33 > .10 0.
X < .125 > .10 3.33 > .10 0.
C < .250 > .10 4.67 > .10 0.
The second column under each type of
entailment in Table 4 lists the ratio of
actual to expected entailments (****
occurs where only the expected is zero; 0
where both expected and actual are zero).
The number of actual and expected
entailments with correlations above the
level in col. (1) are summed for each
level of exceptions. The exception level
with the highest ratio of actual to
expected is then determined and given on
the console as follows:
BEST EXCEPTIONS LEVEL IS .250
AT SIGNAL TO NOISE RATIO OF 4.667
- 19 -
Thus, at 28% exceptions there is a 2:1
ratio of actual to expected entailments
over all four types of entailment.
Referring to col. (2) in Table 3,
however, we see that the ratio of 4.67:1
for strong inclusions is even higher.
These cutoffs determine which entailments
are entered for analysis in the remaining
steps 5 and 6.
6.5 Step 5: Table 5 Transitivity
The entailment structure of MGS is built
by entering entailments which passed the
signal detection test. They are entered
in order of strength, based on (1)
fewest exceptions and (2) highest
relevance, or correlations adjusted for
missing data (see advanced options).
They are now subjected to a further test
of whether (3) transitivity is preserved
with respect to all previously entered
entailments.
The order in which entailments in the
sample data are either entered or
rejected is shown in Table 5 below, which
will appear on the console:
- 20 -
TABLE5 TRANSITIVITIES
EXCEPTIONS
VARI- | RELEVANCE
ABLES | | LEVEL
X Y | | | INTRANSITIVE TRIPLES:
v v v x y z Pxz > MIN(Pxy,Pxz)
==1== =2= =4= 5 6 7 8 =====9 or 10======
1<- 3 .00 .48 7
3<- 4 .00 .38 5
1<- 2 .00 .34 5
2<- 4 .00 .31 5
1<- 4 .00 .23 5
3<- 2 .14 .37 5
2<- 3 .14 .37 5
3 MIN(.14,.33)
2 MIN(.38,.14)
* also rejected as exceeding the limit
for proportion of exceptions.
This table reads as follows. Under ==1==
is the ordered pair of variables. If one
of the two has a negative sign it
indicates an exclusion or coexhaustion.
Arrows of form <- indicate acceptance;
i.e., these entailments pass the transi-
tivity test. Arrows of form 3
ENTAILMENT CHAINS:
1 <- 2 <- 4
7. Drawing the Entailment Hierarchy.
Each entailment chain forms a hier-
archy from of less frequent items (by
inclusion) entailing more frequent items.
For the example here, the entailment
hierarchy is shown below with the
approximate frequencies of variables at
each level given on the left:
30% 1
___/___\___
50% [_2_______3_]
\ /
90% 4
Here the lines represent arrows going
- 24 -
downward for entailments with zero
errors, and the rectangle represents the
mutual entailment 2 <-> 3, with one
error. At any level of exception there
may be multiple hierarchies of
entailments, all running from low to high
frequency items.
The entailments at differenct levels of
exception form a second hierarchical
structure in the data in the sense that
structures with fewer exceptions are by
definition subsets of structures allowing
more exceptions.
Entailment structures may contain nega-
tive entailments, and require other types
of lines to represent mutual exclusion
and coexhaustion. MGS eliminates coex-
haustives by changing the signs of
certain variables. The entailment
hierarchies may then be represented using
relations of inclusion and exclusion, or
`positive' and `negative' lines.
Coexhaustive sign-signing may also be
suppressed (section 8: col.36).
- 25 -
8. Advanced Options.
Parameters that can be set to govern
the analysis are: (1) alter the number of
cases read; (2) include K additional
cases as uniform absences; (3) alter
transitivity rule; (4) set a margin of
negativity for partial correlations when
using the weakest transitivity rule, (5)
fix the maximum proportion of exceptions
allowed; or (6), the minimum relevance or
correlation allowed; (7) reset the number
of levels of exceptions; or (8), the
number of levels of relevance or
correlation; (9) percentage exceptions to
the smaller of the row or column total
for the exceptions cell; (10) alter
criteria for weighting correlations where
observational data are missing; (11) set
number of replications of the random data
comparison; (12) use an alternative
randomization procedure; (13) reset the
random number seed for random number
subroutine; (14) alter the signal/noise
ratio used as cutoff; (15) write input
data; (16) eliminate coexhaustives by
sign inversion; (17) continue analysis
- 26 -
of another comparable dataset following
the first; (18) exclude (mask) sets of
variables from the actual vs. random data
comparison.
Overriding the defaults for each of these
options is done by entering parameters in
line 1 of the input data, as follows:
TYPE OF PARAMETER CHANGE
Column Default Alter Parameter Number
NUMBER OF OBSERVATIONS?
4-6 end-of-file N = Number to be read 1
7-10 0 Add K blank observatns. 2
TRANSITIVITY?
11 4 Transitivity Criterion 3
12-14 .01 Margin for Partial Cor. 4
EXCEPTIONS & CORRELATIONS
15-17 .99 Maximum Exceptions 5
18-20 .10 Minimum Correlation 6
21-22 N if<100 Levels of Exceptions 7
23-24 10 Levels of Correlations 8
25 0 (no) Exceptions Percentaging 9
26 2 Missing Data Weighting 10
Note: the weighting is the proportion
coded to the power 1/P where P is the
parameter in col. 26.
- 27 -
(Advanced Options, cont.)
Column Default Alter Parameter
RANDOM DATA COMPARISON
27 2 Number of Replications 11
28 0 (no) 1 = Alter Randomization 12
29-31 4.0 Reset Random # Seed 13
32-34 1.0 Signal/Noise Cutoff 14
INPUT/OUTPUT OPTIONS?
35 0 (no) 1 = write input data 15
36 0 (no) 1 = no coexch. sign-chg. 16
37 0 (no) 1 = another dataset 17
MASKING LINES ADDED?
38-39 0 (none) Number of Masking Lines 18
Note: Col. 28. The default randomization
is to scramble the order of the
observations for each variables, keeping
the exact marginal frequencies. The
alternative is to sample the observed
values (with replacement), giving the
same expected marginal frequencies.
Note: Col. 38-39. Masking lines are
placed between lines 2 and 3 of the
normal input structure. Each line may
have up to 20 variables in (20I4) format.
- 28 -
(Note: cont.)
Entailments among all variables given on
a single masking line are ignored in the
signal detection analysis. One use of
masking lines is for sets of variables
which are related by definition. Another
is in testing the hypothesis that the
entailments specified by the masking sets
are sufficient to account for the
observed structure. If so, no additional
entailments should be detected.
ENDNOTES
1. The entailment arrow notation is
changed from previous published material
(section 9), and is now in the reverse
direction of the ordinary implicational
arrow. The new notation is consistent
with the direction in inequality, X < Y,
and subset/superset inclusion, X c Y.
2. Actually, because of the scale error,
only the subchain Y <-- X <-- W is
consistent with rule 3. Rule 4 (section
3.2) is taken as the default test of
transitivity of exceptions (sections 4
and 8) because it is less susceptible to
influence by other scale errors.
- 29 -
9. References to MGS and its Precursors
Burton, M.L., D.R.White, L.A.Brudner. "A
Model of the Division of Labor by Sex."
American Anthropologist 4:227-251. 1977.
Coxon, A.P.M., and C.L. Jones. "Implicative
Relations and Social Class," pp. 161-81 in
Class and Hierarchy: The Social Meaning of
Occupations. London: Macmillan Press. 1979.
D'Andrade, R.G. "A Propositional Analysis
of U.S. American Beliefs about Illness."
K.H.Basso and H.A.Selby, eds., Meaning in
Anthropology, pp. 155-180. 1976.
White, D.R., M.L.Burton, L.A. Brudner.
"Entailment Theory and Method: A Cross-
Cultural Analysis of Sexual Division of
Labor." Behavior Science Research 12: 1-24.
1977.
White, D.R., and H.G.McCann. "Cites and
Fights: Entailment Analysis of the 18th C.
Chemical Revolution," in S.D. Berkowitz and
B. Wellman, eds., Social Structure: Form and
Behavior in Social Life. 1987.
- 30 -
10. References to Guttman Scaling
Guttman, Louis L. "The Basis for Scalogram
Analysis," pp. 60-90 in S.A.Stouffer et al.
(eds.) Measurement and Prediction. Prince-
ton: Princeton University Press.
Lingoes, James.
Maranell, G. M. (ed.) Scaling: A
Sourcebook for Behavioral Scientists.
Chicago: Aldine.
McIver, John P., & Edward G. Carmines.
Unidimensional Scaling. Beverly Hills:
Sage Publications. 1981.
Mokken, R.J. A Theory and Procedure of
Scale Analysis. The Hague: Mouton. 1971.
- 31 -
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"Licensed Software") is licensed to you,
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You do not obtain title to the Licensed
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- 32 -
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OF ANY KIND WITH REGARD TO THE LICENSED
SOFTWARE ARE HEREBY DISCLAIMED, INCLUDING
THE IMPLIED WARRANTIES OF MERCHANTABILITY
AND FITNESS FOR A PARTICULAR PURPOSE.
UNDER NO CIRCUMSTANCES WILL THE
MANUFACTURER OR DEVELOPER OF THE LICENSED
SOFTWARE BE LIABLE FOR ANY CONSEQUENTIAL,
INCIDENTAL, SPECIAL OR EXEMPLARY DAMAGES
EVEN IF APPRISED OF THE LIKELIHOOD OF
SUCH DAMAGES OCCURRING. SOME STATES DO
NOT ALLOW THE LIMITATION OR EXCLUSION OF
LIABILITY FOR INCIDENTAL OR CONSEQUENTIAL
DAMAGES, SO THE ABOVE LIMITATION OR
EXCLUSION MAY NOT APPLY TO YOU.
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Copyright
Copyright (c) 1984-98 Douglas R. White as
an unpublished work. All rights reserved.
Disassembly or decompilation of the
software is prohibited.
WARNING! These materials, including the
software provided with these materials,
are protected under copyright, trade
secret and/or other laws. Unauthorized
duplication, transfer, modification or
use of any of these materials may subject
the offender to civil and/or criminal
action. Criminal penalities for willful
copyright infringement include fines and
imprisonment.
+===== California Data Logic ===========+
P.O. Box 12524
La Jolla, CA 92037-0650
619-457-0077
MGS Version 1.2 Re-Order Number OM1.2A
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