Creating nice SEM diagrams in Powerpoint - the easy way

With five powerpoint shapes, you can create almost any SEM diagram, or at least the diagram below. Just follow the step-by-step guides below, or use this powerpoint template, in which I've included all shapes described below (it's only one slide, see picture). Or, use one of the alternatives at the bottom of the post.



Single headed straight arrow
1) click 'Insert' - 'Shapes'
2) select 'Arrow' under 'Lines'
3) draw
4) right-click on the arrow
5) select 'Format shape'
6) select 'Line style'
7) under 'Arrow settings', select the type and size you would like for the begin and end arrows
8) click 'Close'
9) very good, Daniel-san!

Double headed straight arrow
1) click 'Insert' - 'Shapes',
2) select 'Double headed arrow' under 'Lines',
3) draw
4) right-click on the arrow
5) select 'Format shape'
6) select 'Line style'
7) under 'Arrow settings', select the type and size you would like for the arrow
8) click 'Close'
9) very good, Daniel-san!

Manifest variable
1) click 'Insert' - 'Shapes'
2) select 'Rectangle' under 'Rectangles'
3) draw
4) select the square and just start typing to name the variable 
5) very good, Daniel-san!

Latent variable
1) click 'Insert' - 'Shapes'
2) select 'Oval' under 'Basic Shapes'
3) draw
4) select the circle and just start typing to name the variable
5) very good, Daniel-san!

Double headed curved arrows
Ah, the tricky one! Never use the default 'Curved arrow', it will never look right. Instead:
1) click 'Ínsert' - 'Shapes'
2) select 'Arc' under 'Basic shapes'
3) draw an arc
4) select the rightmost yellow diamond of the arc and drag it to the bottom white square (this should give you the right curve already)
5) right click on the arc
6) select 'Format shape'
7) select 'Line style'
7) under 'Arrow settings', select the type and size you would like for the begin and end arrows
8) click 'Close'
9) very good, Daniel-san!

Alternatives
- Use LaTeX with tikz
- Watch this short video tutorial on creating double head curved arrows in powerpoint: https://www.youtube.com/watch?v=8dAmJxBSLy4

Estimates in LISREL output

Parameter estimates

"In LISREL 7 there are two kinds of standardized solutions: SS (Standardized Solution) and SC (Completely Standardized Solution). In the SS solution the latent variables are scaled to have standard derivations equal to unity; the observed variables are left in their original metric. In the SC solution, the observed as well as the latent variables are standardized."*

For tau (intercepts), a standardized solution is not provided. However, tau does depends on the scale of the observed variable (and on other model parameters). So some kind of standardized solution would be informative.

Obviously, for lambda (factor loadings), standardized and completely standardized solutions are printed, as it depends on the scale of observed and latent variables. For theta-epsilon, only completely standardized estimates are printed, as it only depends on the scale of the observed variables (unstandardized theta epsilon is the (co)variances of the observed variables, unexplained by the factor).



Indicators for model modifications

"When a model does not fit well, the modification indices will often be the most useful way of deciding how to change the model to improve the fit. They give an estimate of how much the chi-square will decrease if a fixed parameter is freed."*

A fitted residual is the observed mean or (co)variance (provided in LISREL input), minus the model implied mean and (co)variance.

"A standardized residual is a fitted residual divided-by the large-sample standard error of the residual."*

Expected change is the predicted estimated change in the parameter when set free, for fixed parameters. I'm not sure by what values expected change is divided to obtain the (completely) standardized estimated change.








* Taken from: Jöreskog, K., & Sörbom, D. (1996). LISREL 8: User's reference guide. Chicago, IL: Scientific Software International, Inc.

On calculation of factor means and item intercepts in LISREL, using ML estimation

Options for identification

Among the options for identifying factor means are:
- Fixing the first items intercept to a constant (in most cases: zero)
- Fixing the latent mean to a constant (in most cases: zero)
- Forcing the intercepts to sum to a constant (in most cases: zero)

The second one is not suitable if you expect latent means to differ, and are interested in latent mean or intercept differences. The first and third one are more suitable in such a case, but offer some challenges as well. The third offers a challenge, because I don't know how to do this in LISREL. The first offers a challenge, because item intercepts have to be interpreted as some kind of deviation from the item with intercept fixed to a constant.



Identification by fixing the first item's intercept to zero

In this case, factor means and item intercepts are very dependent on the item chosen for identification. This is an important consideration if one wants to test an hypothesis concerning factor means, for example in multiple group comparisons. It almost amounts to a test concerning observed means for the items used for identification.

Formulae

Let i denote an item used for identification
Let j denote any other item
Let k denote a factor

Let y_ denote an observed item mean
Let alpha denote a factor mean
Let lambda denote a factor loading
Let tau denote an item intercept

alpha(k) = lambda(i) * y_(i)
tau(j) = y_(j) - lambda(j) * alpha(k)

When the model is identified by constraining the first items intercept to 0, and the first items loading to 1 is used, this simplifies to:

alpha(k) = y_(i)
tau(j) = y_(j) - lambda(j) * y_(i)

In words

The factor mean equals the observed mean of the identification item. Other items intercepts are determined by the items factor loading, times the identification items observed mean. An illustration is provided below, for a model of 3 factors fitted to 2 groups.


Examples

Values are taken from LISREL in- and output provided below. Small discrepancies arise from rounding.

1)
The first item is used as an identification item for the first factor.
In the first group, the item intercept for the second item (item 2) of the first factor is calculated as follows:
y_(item1) = 0.425 = alpha(factor1)
tau(item2) = 0.10 = y_(item2) - lambda(item2)*y_(item1) = 0.511 - 0.98*0.425

2)
The fourth item is used as an identification item for the second factor. In the second group, the item intercept for the second item of factor 2 is calculated as follows:
y_(item1) = 0.673 = alpha(factor2)
tau(item11) = -0.01 = y_(item11) - lambda(item11)*y_(item4) = 0.511 - 0.71*0.673


LISREL input

Observed means (y_; item 1-21):

G1: 0.425 0.511 0.488 0.618 0.380 0.320 0.611 0.582 0.182 0.222 0.406 0.389 0.387 0.602 0.530 0.570 0.588 0.092 0.042 0.206 0.375

G2: 0.566 0.459 0.475 0.673 0.289 0.275 0.590 0.559 0.247 0.288 0.474 0.463 0.343 0.553 0.422 0.603 0.494 0.202 0.023 0.217 0.642


Factor pattern (item 1-21):

item factor
1 1
2 1
3 1
4 2
5 1
6 1
7 1
8 1
9 1
10 1
11 2
12 2
13 2
14 1
15 2
16 3
17 2
18 3
19 3
20 2
21 3


LISREL output

Estimated factor means (alpha, factor 1-3):
G1: 0.425 0.618 0.570
G2: 0.566 0.673 0.603


Estimated item intercepts (tau):

item G1 G2

factor 1
1 0.00 0.00
2 0.10 -0.14
3 0.01 -0.23
5 0.03 -0.10
6 0.01 -0.34
7 0.11 -0.26
8 0.19 -0.40
9 0.05 -0.20
10 0.01 -0.13
14 0.16 -0.14

factor 2
4 0.00 0.00
11 0.05 -0.01
12 0.06 0.04
13 0.11 -0.21
15 0.09 -0.09
17 0.00 0.10
20 0.11 0.14

factor 3
16 0.00 0.00
18 0.23 -0.21
19 0.21 -0.04
21 0.16 -0.15


estimated factor loadings (lambda):

item G1 G2

factor 1
1 1.00 1.00
2 0.98 1.07
3 1.12 1.24
5 0.83 0.68
6 0.78 1.09
7 1.18 1.50
8 0.92 1.70
9 0.54 0.79
10 0.51 0.74
14 1.03 1.23

factor 2
4 1.00 1.00
11 0.57 0.71
12 0.72 0.63
13 0.81 0.82
15 1.00 0.75
17 0.96 0.58
20 0.15 0.12

factor 3
16 1.00 1.00
18 0.56 0.69
19 0.45 0.11
21 0.94 1.31