Supplemental Digital Content
Psychosomatic Medicine: Close relationships and health in daily life: A review and empirical
data on intimacy and somatic symptoms
Index
Appendix A: Detailed Description of the Analysis in Model C
Appendix B: Explanation of the Toeplitz Error Variance Covariance Structure
Appendix C: Syntax in SAS 9.2 and Data Structure
Appendix D: Reversing the Order of Prediction: Change in Intimacy From Yesterday to Today
Predicted By Prior and Concurrent Change in Symptoms
Appendix A: Detailed Description of the Analysis in Model C: Differential Effects of Prior and
Concurrent Increase and Decrease in Intimacy on Symptom Change
To explore asymmetrical effects of changes in intimacy, i.e., if increasing intimacy and
decreasing intimacy have different effects on symptom change, Model C shown in Equation 4 in
the article was fit to the data:
(SYMit – SYMit-1) = 00 + 01 DAYc18it + 02 (INTit-1 –INTit-2) + 03 (INTit –INTit-1)
+ 04 (INTit-1 –INTit-2)*UPi(t-1)-(t-2) + 05 (INTit –INTit-1)*UP it-(t-1) + it
(4)
Model C represents a piecewise linear
regression (also called spline function,
(1)). The idea behind piecewise
regression is to divide the predictor into
segments of linear slopes that are
connected at one or several break points,
called knots. Model C has one knot at
zero change in intimacy, allowing the
influence of intimacy to vary depending
on whether it takes on negative or
positive values. Figure 1 shows an
example for a piecewise linear
regression: Prior intimacy increase and
decrease have asymmetric effects on
symptom change, as reported in the
article.
Figure 1. Prior within-person change in intimacy predicts subsequent within-person change in
symptoms: When prior intimacy increases, symptoms decrease subsequently; when prior
intimacy decreases, however, subsequent symptoms are unrelated.
Model C includes two indicator variables, UPi(t-1)-(t-2) for prior increase in intimacy, and UP it-(t-1)
for concurrent increase in intimacy. These indicators were coded 0 when intimacy decreased or
did not change, and +1 when intimacy was going up. Including the two indicator variables in the
model allows for piecewise regression by changing the meaning of the slopes, 02 (INTit-1 –INTit2) and 03 (INTit –INTit-1).
To explain how these two indicator variables work, we want to remind readers of the meaning of
both intimacy slopes without the indicator variables (see the first line of Equation 4). Figure 2
shows the effects of intimacy change on symptom change without taking potential asymmetry
into account. Without taking asymmetry into account, the slope for prior change in intimacy, 02
(INTit-1 –INTit-2), has the same meaning as in Equation 2 and 3 in the article. This slope indicates
how much symptoms change with prior change in physical intimacy from two days ago to
yesterday. The slope for concurrent change in intimacy, 03 (INTit –INTit-1), has the same
meaning as in Equation 3 in the article. This slope indicates how much symptoms change when
concurrent intimacy changes. Conceptually, we assume with these linear slopes that intimacy
increase and decrease have symmetrical effects on symptom change. Without the indicator
variables, these two slopes assume a linear relationship between predictors and outcome that
Figure 2 represents as a straight line.
Figure 2. Within-person change in intimacy predicts within-person change in symptoms: When
intimacy goes up, symptoms go down subsequently and concurrently (as the graph for lagged
change and the graph for concurrent change show).
Next, we focus on the second line in Equation 4 that shows two interactions that contain the
indicator variables. The first interaction, (INTit-1 –INTit-2)*UPi(t-1)-(t-2), contains the predictor prior
intimacy change and an indicator variable representing increasing prior intimacy. When prior
intimacy does not increase (when prior intimacy decreases or does not change), the indicator
variable equals zero and the interaction disappears from the equation. When prior intimacy
increases, the indicator variable equals 1 and the effect 04 (INTit-1 –INTit-2)*UPi(t-1)-(t-2) represents
how much the slope for increasing prior intimacy differs from the slope for decreasing prior
intimacy. The second interaction, 05 (INTit –INTit-1)*UP it-(t-1), contains the predictor concurrent
intimacy change and the second indicator variable representing increasing concurrent intimacy.
When concurrent intimacy does not increase (when concurrent intimacy decreases or does not
change), the indicator variable equals zero and the interaction disappears from the equation.
When concurrent intimacy increases, the indicator variable equals 1 and the effect 05 (INTit –
INTit-1)*UP it-(t-1) represents how much the slope for increasing concurrent intimacy differs from
the slope for decreasing concurrent intimacy. Adding these interactions to Equation 4 changes
the meaning of the slopes for prior and concurrent intimacy, 02 (INTit-1 –INTit-2) and 03 (INTit –
INTit-1). As in all regression models with higher-order interactions, the main effects now
represent conditional effects when higher-order interactions that contain these predictors equal
zero (2, p. 259 - 262). In Equation 4, the slopes now are conditional effects when their respective
indicator variable for increasing intimacy equals zero, i.e., when intimacy decreases or does not
change.
For example, if we focus for the moment on prior intimacy change and separate the segment for
decreasing intimacy, (INTit-1 –INTit-2)  0, from the segment for increasing intimacy, (INTit-1 –
INTit-2) > 0, we can split up Equation 4 into two piecewise linear regression equations (see
Equation 5a and 5b):
If (INTit-1 –INTit-2)  0
(SYMit – SYMit-1) = 00 + 01 DAYc18it + 02 (INTit-1 –INTit-2) + it
If (INTit-1 –INTit-2) > 0
(SYMit – SYMit-1) = 00 + 01 DAYc18it + 02 (INTit-1 –INTit-2)
+ 04 (INTit-1 –INTit-2)*UPi(t-1)-(t-2) + it
(5a)
(5b)
When prior intimacy decreases, the interaction with the upwards indicator is 0 and drops from
the equation (Equation 5a). When prior intimacy increases (Equation 5b), the upwards indicator
is 1 and the slope for increasing intimacy is the sum of 02 and 04 (Equation 5c). Therefore, 04
tests if the slope for increasing intimacy is significantly different from the slope for decreasing
intimacy.
02 (INTit-1 –INTit-2) + 04 (INTit-1 –INTit-2)*UPi(t-1)-(t-2) =
02 (INTit-1 –INTit-2) + 04 (INTit-1 –INTit-2)*1 =
(02 + 04 )(INTit-1 –INTit-2)
(5c)
In sum, including the two indicator variables in interaction terms allowed different slopes for
decreasing and increasing intimacy. With these interactions included, 02 and 03 represent the
effects of decreasing prior and concurrent intimacy, whereas 04 and 05 represent how much the
effects of increasing prior and concurrent intimacy differ from the effects of decreasing prior and
concurrent intimacy. Significant effects for these interactions indicate that the slope for
increasing intimacy is different from the slope for decreasing intimacy. Figure 1 represents this
asymmetry as a line with a break point at zero intimacy change.
Appendix B: Explanation of the Toeplitz Error Variance Covariance Structure
A Toeplitz structure with two bands was assumed for the residual error matrix in Model A, B,
and C to account for remaining autocorrelation. Data exploration revealed that the symptom data
showed substantial autocorrelation (r = -.48, see Table 2 in the article). As recommended by
Singer and Willett (3), we considered using several error covariance structures. We initially
chose a Toeplitz structure with multiple bands to allow for autocorrelation across several days.
We found substantial residual autocorrelation for lag 1 (between change from yesterday to today
and prior change from 2 days ago to yesterday) that rapidly decayed to close to 0 for lag 2, lag 3,
and so on up to lag 32, indicating that a single covariance band accurately reflected
autocorrelation in these data. Therefore, we used a Toeplitz structure with two bands (a single
variance band and a single covariance band), as shown in Table 1. The error variance-covariance
matrix shows residual variances and covariances for 33 days and is very parsimonious: It
contains a single diagonal variance parameter, 2 (marked by the yellow diagonal) reflecting the
assumption that all 33 timepoints have equal residual variance, and a single off-diagonal
covariance parameter, 1 (marked in orange), reflecting the assumption of constant
autocorrelation between two adjacent time points, and no further autocorrelation, as all higher
bands are set to 0.
Table 1. Error Variance-Covariance Matrix With Banded Toeplitz Structure, TOEP(2).
T1
T2
T3
T1
T2
T3
T4
T5
2
1
0
0
0
1
2
1
0
0
0
1
2
1
0
T31
T32
T33
0
0
0
0
0
0
0
0
0
T4
0
0
1
2
1
0
0
0
T5
0
0
0
T32
0
0
0
0
0
T33
1
2
T31
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
1
2
0
0
0
0
0
We decided against using a more conventional first-order autoregressive structure, AR(1), as
shown in Table 2, because in the presence of substantial negative autocorrelation an AR(1)
structure produces an implausible pattern. The AR(1) structure would be equally parsimonious as
the Toeplitz structure: It contains a single diagonal variance parameter, 2 (marked by the yellow
diagonal) reflecting the assumption that all 33 timepoints have equal residual variance, and a
single parameter for autocorrelation, (cells containing marked in orange), that also produces
a banded structure, with 2 in the first covariance band, 22 in the second covariance band,
and 32 off-diagonal covariance parameter, reflecting the assumption of constant
autocorrelation between two adjacent time points that gets weaker and weaker with further lags.
In the presence of substantial negative autocorrelation, such as r = -0.48, an AR(1) structure
would accurately reflect the first covariance band (lag 1),  For the second covariance
band (lag 2), this structure would show considerable positive autocorrelation, 2 = -0.48*-0.48 =
0.23. For the third covariance band (lag 3), this structure would show negative autocorrelation
again, 3 = -0.48*-0.48*-0.48 = -0.11. For the fourth covariance band (lag 4), this structure
would show positive autocorrelation, 4 = -0.48*-0.48*-0.48*-0.48 = 0.05. The changing sign of
autocorrelation and the slower decay of autocorrelation across lags in the AR(1) structure do not
reflect the error covariance structure of the data, as our initial data exploration showed.
Table 2. Error Variance-Covariance Matrix With First-Order Autoregressive Structure, AR(1).
T2
2
2
2
22
32
T3
22
2
2
2
22
T4
T1
T2
T3
T4
T5
T1
2
2
22
32
42
T31
T32
T33
302
312
322
292
302
312
282
292
302
272
282
292

22
2
2
2
3 2
T5
42
32
22
2
2
T31
302
292
282
272
262
T32
312
302
292
282
272
T33
322
312
302
292
282
262
272
282
2
2
22
2
22
2
2
2
2
UN@AR(1) is one standard way of modeling an error variance-covariance matrix that also
accounts for dyadic dependencies (4) that is easily implemented in SAS. In our case, the error
variance-covariance matrix would require a UN@Toep(2) structure that is not a standard option
in SAS or other software packages and is not straightforward to implement. As the dependency
between partners was very limited, we chose to model the error covariance matrix on the
individual level with a simpler Toep(2) structure.
Appendix C: Syntax in SAS 9.2 and Data Structure
*Syntax documentation
SAS 9.2 code for analyses in the article: “Close Relationships and Health in
Daily Life: A Review and Empirical Data on Intimacy and Somatic Symptoms”
For Psychosomatic Medicine’s Special Issue on Ambulatory Monitoring in the
Section “Selected domains: Social environments” ;
*use rectangular data set that has the same number of lines per person, in
this case 35 lines per participant,
i.e., the data set has empty lines if a participant missed a certain day ;
data DataIntSymps1 ;
set "c:\data\DataIntSymps" ;
*create time variable diaryday33_c18
diaryday1_35 is centered at the middle of the diary period (Day 18)
and rescaled to represent the whole diary period of 33 days (Day 3 to 35)
facilitating the interpretation of the time coefficient
that is otherwise very small ;
diaryday_c18std33 = (diaryday1_35 - 18)/33 ;
*create symptom lag variables and variable for symptom change ;
Symplag1 = lag(Symp) ;
Symplag2 = lag(Symplag1) ;
SympChange = Symp - Symplag1 ;
PriorSympChange = Symplag1 - Symplag2 ;
*create upwards indicator for prior and concurrent change in intimacy ;
IF SympChange>0 THEN SympChangeUp =1 ;
IF SympChange<=0 AND (SympChange > .) THEN SympChangeUp=0 ;
IF SympChange = . THEN SympChangeUp= . ;
IF PriorSympChange>0 THEN PriorSympChangeUp =1 ;
IF PriorSympChange<=0 AND (PriorSympChange > .) THEN
PriorSympChangeUp=0 ;
IF PriorSympChange= . THEN PriorSympChangeUp = . ;
*create intimacy lag variables and variable for intimacy change ;
Intlag1 = lag(Int) ;
Intlag2 = lag(Intlag1) ;
IntChange = Int - Intlag1 ;
PriorIntChange = Intlag1 - Intlag2 ;
*create upwards indicator for prior and concurrent change in intimacy ;
IF IntChange>0 THEN IntChangeUp=1 ;
IF IntChange<=0 AND (IntChange > .) THEN IntChangeUp=0 ;
IF IntChange = . THEN IntChangeUp= . ;
IF PriorIntChange>0 THEN PriorIntChangeUp=1 ;
IF PriorIntChange<=0 AND (PriorIntChange > .) THEN PriorIntChangeUp=0 ;
IF PriorIntChange = . THEN PriorIntChangeUp= . ;
run ;
*Choose Day 3 to 35 for these analyses because we were using lag2 variables ;
data DataIntSymps2 ;
set DataIntSymps1;
if diaryday1_35 >= 3 ;
run ;
*Prior and concurrent intimacy change predicting symptom change ;
*Model A: Prior change in intimacy predicts subsequent change in symptoms ;
PROC MIXED data = DataIntSymps2 covtest empirical ;
class id diaryday1_35 ;
model SympChange = diaryday_c18std33 PriorIntChange /s ddf = 161, 161, 161 ;
Repeated diaryday1_35 / subject=id Type = TOEP(2) r=21 rcorr=21 ;
TITLE 'Model A Total symptom change from yesterday to today predicted by
prior change in intimacy';
run ;
*Model B: Prior and concurrent change in intimacy predict change in symptoms
;
PROC MIXED data = DataIntSymps2 covtest empirical ;
class id diaryday1_35 ;
model SympChange = diaryday_c18std33 PriorIntChange IntChange /s ddf = 160,
160, 160, 160 ;
Repeated diaryday1_35 / subject=id Type = TOEP(2) ;
TITLE 'Model B Total symptom change from yesterday to today predicted by
prior and concurrent change in intimacy';
run ;
*Model C: Asymmetry of increase and decrease in intimacy predicting change in
symptoms ;
PROC MIXED data = DataIntSymps2 covtest empirical ;
class id diaryday1_35 ;
model SympChange = diaryday_c18std33 PriorIntChange IntChange
PriorIntChange*PriorIntChangeUp IntChange*IntChangeUp /s ddf = 158, 158, 158,
158, 158 ;
Repeated diaryday1_35 / subject=id Type = TOEP(2) r=21 rcorr=21 ;
TITLE 'Total symptom change from yesterday to today predicted by concurrent
and prior change in intimacy';
run ;
*We need to calculate the correlation because SAS outputs the covariance s1
Source: SAS/STAT(R) 9.2 User's Guide, Second Edition, Repeated Statement
http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.
htm#statug_mixed_sect019.htm
TOEP(2)
id
-0.3329
Residual
0.6945
=> r =
covXY / SQRT(VARX x VARY) = -0.3329 / SQRT (0.6945 * 0.6945) =
= -.48
autocorrelation is the covariance of today (Day t) and yesterday (Day t-1),
divided by the pooled standard deviation = SQRT of both variances
We get the residual autocorrelation also with the rcorr= statement,
here for participant 21 ;
Table 3. Data Structure
Day_c18
Symp
Int
PriorInt
Int
PriorInt
ID Day1_35 Day_c18
std33
Symp Symplag1 Symplag2 Change Int Intlag1 Intlag2 Change Change ChangeUp
ChangeUp
1
1
-17
-0.52
2
0.75
1
2
-16
-0.48
1
2
-1
0.25
0.75
-0.5
0
1
3
-15
-0.45
1
1
2
0
0.25
0.25
0.75
0
-0.5
0
0
1
4
-14
-0.42
1
1
1
0
0.75
0.25
0.25
0.5
0
1
0
1
5
-13
-0.39
1
1
0.75
0.25
0.5
1
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
1
16
-2
-0.06
0
0
0
0
0.25
0.25
0.25
0
0
0
0
1
17
-1
-0.03
0
0
0
0
0.75
0.25
0.25
0.5
0
1
0
1
18
0
0.00
0
0
0
0
0.25
0.75
0.25
-0.5
0.5
0
1
1
19
1
0.03
0
0
0.25
0.75
-0.5
0
1
20
2
0.06
0
0.25
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
1
31
13
0.39
2
0
1
2
0.75
0.25
0.75
0.5
-0.5
1
0
1
32
14
0.42
0
2
0
-2
0.25
0.75
0.25
-0.5
0.5
0
1
1
33
15
0.45
0
2
0.25
0.75
-0.5
0
1
34
16
0.48
0
0.25
1
35
17
0.52
1
0.25
2
1
-17
-0.52
1
1
0
0.75
0.25
0.5
1
2
2
-16
-0.48
1
1
1
0
0.75
0.75
0.25
0
0.5
0
1
2
3
-15
-0.45
1
1
1
0
0.25
0.75
0.75
-0.5
0
0
0
2
4
-14
-0.42
0
1
1
-1
0.75
0.25
0.75
0.5
-0.5
1
0
2
5
-13
-0.39
0
1
0.75
0.25
0.5
1
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
Note. The variables used in the main analyses are marked in yellow. The first two diary days are marked in grey because they were excluded from the analyses due to
the use of lagged variables. ID = participant id. Day1_35, Day_c18, and Day_c18std33 are indicating diary day, first ranging from Day 1 to 35, second centered on
Day 18, and third when centered on Day 18 and rescaled so that one unit increase indicates the whole diary period of 33 days. Symp represents the number of
symptoms per day, Symplag1 and Symplag2 represent symptoms lagged by one and two days, i.e., yesterday’s symptoms and symptoms two days ago. Symp Change
represents the difference between yesterday’s and today’s symptoms. Intimacy is physical intimacy rated on a 1 to 5 scale and rescaled to a 0 to 1 range. Intlag1 and
Intlag2 represent symptoms lagged by one and two days, i.e., yesterdays intimacy and intimacy two days ago. IntChange represents the difference between
yesterday’s and today’s intimacy. PriorIntChange represents the difference between intimacy two days ago and yesterday. IntChangeUp and PriorIntChangeUp
represent upwards change indicators that take on the value 1 when intimacy change takes on a positive value and are otherwise 0.
Appendix D: Reversing the Order of Prediction: Estimates For Change in Intimacy From Yesterday to Today Predicted By Prior and
Concurrent Change in Symptoms
Model A: Prior
Change
Fixed Effects
Intercept for Day 18
Model B: Prior and
Concurrent
Change
Model C: Differential
Effects of Prior and
Concurrent Increase and
Decrease
00 
γ (SE)
0.001 (0.001)
γ (SE)
0.001 (0.001)
0.000
γ (SE)
(0.002)
Day, centered at Day 18
DAYc18it
01 
0.007
(0.004)
0.008
(0.004)
0.010
(0.004)
Prior Change in Symptoms
SYMit-1 –SYMit-2
02 
-0.003
(0.006)
-0.003
(0.006)
-0.003
(0.006)
Concurrent Change in
Symptoms
SYMit –SYMit-1
03 
-0.021
(0.006)*
-0.023
(0.008)*
Prior Increase in Symptoms
(SYMit-1 –SYMit-2)*UPi(t-1)-
04 
-0.001
(0.003)
05 
0.009
(0.012)
(t-2)
Concurrent Increase in
Symptoms
(SYMit –SYMit-1)*UP it-(t-1)
Random Effects
Autocorrelation
Residual
* p <. 05. N = 164
Estimate (SE)
TOEPLITZ


-0.48
(0.010)*
-0.48
(0.010)*
-0.48
(0.010)*
it
0.69
(0.018)*
0.69
(0.018)*
0.69
(0.018)*
To test if prior symptom change predicted subsequent intimacy change, we ran additional models
where prior and concurrent changes in symptoms were predictors and change in intimacy was the
dependent variable, reversing the order of prediction from the main analyses reported in the
article’s Table 2. As expected, the only significant finding was the concurrent association of
change in symptoms and intimacy, 03, replicating the findings in Table 2. The model found no
support for effects of prior change in symptoms on subsequent change in intimacy.
Equation 6 shows Model A:
(6)
(INTit –INTit-1) = 00 + 01 DAYc18it + 02 (SYMit-1 –SYMit-2) + it
Change in intimacy from yesterday to today, INTit –INTit-1, is predicted by diary day centered at
Day 18, DAYc18it, and prior symptom change from two days ago to yesterday, SYMit-1 –SYMit-2.
Equation 7 shows Model B.
(INTit –INTit-1) = 00 + 01 DAYc18it + 02 (SYMit-1 –SYMit-2) + 03 (SYMit – SYMit-1) + it (7)
Concurrent change in symptoms from yesterday to today, SYMit – SYMit-1, is added as a predictor
to Model B.
Equation 8 shows Model C:
(INTit –INTit-1) = 00 + 01 DAYc18it + 02 (SYMit-1 –SYMit-2) + 03 (SYMit – SYMit-1)
+ 04 (SYMit-1 –SYMit-2)*UPi(t-1)-(t-2) + 05 (SYMit – SYMit-1) *UPit-(t-1) + it
(6)
The indicator variables UPi(t-1)-(t-2) and UPit-(t-1) in Model C stand for increase in prior and
concurrent symptoms. Including these indicator variables as interaction terms with prior and
concurrent symptom change in the equation influences the interpretation of the predictors: The
two main effects, SYMit-1 –SYMit-2 and SYMit – SYMit-1, represent the effects of prior and
concurrent symptom decrease, and the interaction terms, (SYMit-1 –SYMit-2)*UPi(t-1)-(t-2) and
(SYMit – SYMit-1) *UP it-(t-1), represent how much the effects of prior and concurrent symptom
increase differ from the effects of prior and concurrent symptom decrease.
1.
2.
3.
4.
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