ERRATA
Shipley, B. (2000). Cause and Correlation in Biology. A user’s guide to
path analysis, structural equations and causal inference. Cambridge University
Press.
Updated March 28, 2002. Please inform me (bshipley@courrier.usherb.ca)
of any other errors.
Page 24
Replace the following sentence (last paragraph):
… I develop a translation device to move between causal models and
observations (statistical) models.
With the following sentence:
… I develop a translation device to move between causal models and
observational (statistical) models.
Page 28:
Replace the following sentence:
… the natural state of a noncollider is the active (ON) state and the
natural state of a noncollider is the inactive (OFF) state.
With the following sentence:
… the natural state of a noncollider is the active (ON) state and the
natural state of a collider is the inactive (OFF) state.
Page 31:
Table 2.1. Replace the following sentence:
I(X,{U,W},Y).
With the following sentence:
~I(X,{U,W},Y).
Page 33:
Replace the following sentence:
If (X,F ,Y) then P(X,Y)=P(X)xP(Y)
With the following sentence:
If I(X,F ,Y) then P(X,Y)=P(X)xP(Y)
Page 48:
Replace the following sentence (last paragraph):
… it is useful briefly to look at what philosophers of science…
With the following sentence:
… it is useful to briefly look at what philosophers of science…
Page 72:
Replace the following sentence:
… {(A,C), (A,D), (A,E), (A,F), (B,E), (B,F), (C,D), (C,F), (D,F), (E,F)}.
With the following sentence:
… {(A,C), (A,D), (A,E), (A,F), (B,E), (B,F), (C,D), (C,F), (D,F)}.
Page 73:
Table 3.1 Delete the last line (beginning with E,F) of this table
Page 80:
Replace the following sentence (last paragraph):
The middle graph show the same complicated nonlinear function in the range 1
to 3 of the X values and the middle graph shows this in the range 1.5 to 2.5 of
the X values.
With the following sentence:
The middle graph shows the same complicated nonlinear function in the range
1 to 3 of the X values and the graph to the right shows this in the range 1.5 to
2.5 of the X values.
Page 105:
Replace the following equations:
With the following equations:
Page 113:
Replace the following sentence (last paragraph):
… which we group together in a vector , we
will write the population covariance matrix as .
With the following sentence:
… which we group together in a vector , we
will write the model covariance matrix as .
Page 115:
Replace the following formula:
With the following formula:
Page 128:
Replace the following table heading:
Table 4.5. Decomposition of the total association between each pair of
variables in Figure 4.5 into direct effect,…
With the following table heading:
Table 4.5. Decomposition of the total association between each pair of
variables in Figure 4.7 into direct effect,…
Page 156:
Replace the following sentence (first paragraph):
… answered ‘[c]oncepts have the same reality of lack or reality as other
ideas…
With the following sentence:
… answered ‘[c]oncepts have the same reality or lack of reality as other
ideas…
Page 169171 (Box 6.1):
Replace the text in this box by the following: Note that the IDEN program
uses the correct formulation (below) of the FC1 rule for structural
identification of a measurement model.
The FC1 ("Factor Complexity 1") rule for the structural
identification of a measurement model assumes that each observed
indicator variable is caused by only 1 latent variable (hence its name).
For each latent variable, L_{i}, in the measurement model,
construct a binary matrix P_{i} with q_{i} rows
and t columns; q_{i} is the number of observed indicator
variable of L_{i} and t is the total number of observed
indicator variables in the model. Each element (p_{ij}) of P_{i}
has a 1 if the error variables of indicators i and j are dseparated or
if the covariance between then has been fixed and if the covariance of
the latents associated with indicator variables i and j are free.
Form the matrix D_{i}=P_{i}P’_{i}.
Iteratively multiply until you get the
matrix .
The first requirement for structural identification is that every
element of be nonzero in the row
corresponding to the indicator of L_{i} that defines its scale.
This must be true for all latent variables in the model.
The second requirement for structural identification of the full
measurement model is that, for every pair of latent variables whose
covariance is to be estimated (i.e. that are not dseparated or whose
covariance is not fixed) there must be at least one pair of indicator
variables (one for each latent) whose error variables are independent
(i.e. dseparated) or whose covariance is fixed.
The third requirement for structural identification of the full
measurement model is that, for every latent variable whose variance is
to estimated (i.e. is not fixed), there must be at least one pair of
indicator variables (one for each latent) whose error variables are
independent (i.e. dseparated) or whose covariance is fixed.
I will now show how this rule works with reference to Figure 6.3.
In this model there are two latent variables, so we need two P
matrices:
Note that p_{12}=p_{21}=1 in P_{1}
because e _{1}has a fixed (zero)
covariance with e _{2} and similarly
for e _{4} and e
_{5} in P_{2}. There are three indicator
variables for each latent and so q_{1}=q_{2}=3. We must
form and .
These are the same in this example, although this is not true in
general:
.
Now, the first requirement is that every element in the row of each
matrix representing the scaling variable must be nonzero. The scaling
variable of the first latent variable is X_{1} and so every
element in row 1 of the first matrix must be nonzero. The first part of
this first requirement is fulfilled. The scaling variable of the second
latent variable is X_{4} and so every element in row 1 of the
second matrix must be nonzero. The second part of this first
requirement is also fulfilled.
The next requirement is that there be at least one pair of error
variables (one associated with an indicator of each unique pair of
latents) whose covariance is zero or fixed to some other value. Error
variables e _{2} and e
_{5} fulfill this second requirement.
The final requirement is that there must be at least one pair of
error variables (associated with an indicator of each latent) whose
covariance is zero or fixed to some other value. Error variables e
_{1} and e _{2} fulfill this
requirement for the first latent variable and error variables e
_{4} and e _{5} fulfill this
requirement for the second latent variable. Therefore this measurement
model is structurally identified.
Page 177, bottom of last full paragraph:
Replace the following text:
" Since these simulated data sets are mutually independent and
large in number you can obtain a 95% confidence interval (Manly 1997)
around p by referring to a normal distribution whose mean is (xNp)
and whose standard deviation is Np(1p). Thus the 95% confidence
interval is p± 1.96Np(1p)."
With the following text:
" Since these simulated data sets are mutually independent and
large in number you can obtain a 95% confidence interval (Manly 1997)
around p by referring to a normal distribution whose mean is x
and whose variance is Np(1p). Thus the 95% confidence interval
is ."
Page 178:
Replace the following text:
Given a desired degrees of freedom (df) find a value for v such
that d£ v(v+1)/2 and d³
v(v1)/2. Call this v^{*}. For instance, if we want df=9 then
choose v*=4 since v(v1)/2=6 and v(v+1)/2=10.
Calculate c=df=v^{*}. So, if we want df=9 then c=96=3.
With the following text:
Given the desired degrees of freedom (df), find the smallest
integer value of v such that df£ v(v+1)/2.
This will be the smallest integer value of v such that .
For example, if df=9 then we need the smallest integer value of v such
that . Thus v=4.
Find the integer value of c such that c=v(v+1)/2 – df. So, if df=9 and v=4
then c=1.
Page 234:
Replace the following header to Box 7.2:
Variance components in a nested box
With the following header:
Variance components in a nested ANOVA
Page 243 (point 1, bottom of page):
Replace the following sentence:
… then draw a line (not an arrow) between the pair.
With the following sentence:
… then draw a line (not an arrow) between the pair; see inducing paths
(pp. 250253).
Page 254:
Replace the following sentence:
… a line between Y and Z (X—Z—Y), but no line between X and Z.
With the following sentence:
… a line between Y and Z (X—Z—Y), but no line between X and Y.
