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LATENT DIFFERENCE SCORES FOR DISCREPANCIES 1
Latent Difference Score modeling: A Flexible Approach for Studying Informant
Discrepancies
Amaranta de Haan, PhD1
Prof. Peter Prinzie1
Miranda Sentse, PhD2
Joran Jongerling, MSc1
1 Erasmus University Rotterdam,
Department of Psychology, Education & Child Studies
2 Leiden University
Institute of Criminal Law and Criminology
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 2
Abstract
The current study proposes a flexible approach to studying informant discrepancies: Latent
Difference Scores modeling (LDS). The LDS approach is demonstrated using an empirical
example in which associaitons between mother-adolescent and father-adolescent discrepant
parenting perceptions, and concurrent and later adolescent externalizing behaviors were
investigated. Early adolescents (N=477, aged 12-15 years), mothers (N=470), and fathers
(N=440) filled out questionnaires about mothers’ and fathers’ parenting. Results using the
LDS approach are compared to results obtained by the two existing approaches for informant
discrepancies: Observed Difference Scores modeling (ODS) and Polynomial Regression
Analyses (PRA).
Results from the LDS approach show that adolescents perceive their mothers’ and
fathers’ parenting less favorably than mothers and fathers themselves, and that stronger
mother-adolescent discrepancies are consistently related to stronger father-adolescent
discrepancies. Parent-adolescent discrepancies were concurrently associated with more
aggressive and rule-breaking behaviors, but not longitudinally. Results generalized across the
two discrepancy approaches, but only very few significant associations were found in the
PRA. Advantages and limitations of all three approaches to studying informant discrepancies
are discussed.
Keywords: Informant discrepancies; Latent Difference Score modeling; Observed Difference
Score modeling; Polynomial Regression Analyses; parenting; adjustment problems; early
adolescence; gender; age
Public Significance Statement. This study shows that parents perceive their own behaviors
more favorably (i.e., higher levels of positive parenting, lower levels of negative parenting)
than adolescents view parents’ behaviors. Mother-adolescent and father-adolescent discrepant
perceptions of different types of parenting are consistently interrelated, and parent-child
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 3
disagreement is associated with concurrent but not later levels of aggressive and rule-breaking
behaviors.
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 4
Latent Difference Score modeling: A Flexible Approach for Studying Informant
Discrepancies
The use of multiple informants’ reports on the same behaviors are considered key components
of best practices in psychological assessment (Hunsley & Mash, 2007). Nevertheless,
inconsistencies often arise among mulitple informants’ reports (hereafter referred to as
“informant discrepancies”), even if informant complete parallel or identical measures
(Achenbach, 2006; De Los Reyes, 2011). Rather than statistical nuisance, however, informant
discrepancies can have substantive meaning above and beyond individual informant reports.
Given that discrepancies can be viewed as worthwhile units of analysis, developing
(statistical) approaches that can adequately assess informant discrepancies is of paramount
importance (Laird & De Los Reyes, 2013). Until now, informant discrepancies have been
examined using either of two approaches: Observed Difference Scores (ODS; see e.g., De Los
Reyes & Kazdin, 2004) or Polynomial Regression Analyses (PRA; Laird & De Los Reyes,
2011). Unfortunately, the validity of ODS is seriously hampered by a number of
methodological issues. Further, the types and complexity of research questions that can be
addressed using PRA is rather limited.
The current study proposes a flexible alternative to studying informant discrepancies,
the Latent Difference Scores (LDS) approach. The utility of the LDS approach is
demonstrated in an empirical example, in which interrelations between mother-adolescent and
father-adolescent discrepant perceptions of parenting are examined, and their simultaneous
associations with concurrent and later adolescent adjustment problems are investigated.
Second, to provide more comprehensive knowledge about the comparability of the different
approaches, associations between parent-child discrepancies and adjustment problems
obtained by ODS and PRA are also investigated.
Approaches for Studying Informant Discrepancies
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 5
Informant discrepancies are typically examined using ODS, but unfortunately, this
approach is plagued by several several methodological issues. Because ODS are a
combination of two variables that are both measured with error, they have inflated
unreliability, which may result in downwardly biased parameter estimates (Edwards, 2002;
but, see Thomas & Zumbo, 2012). Further, if measurement invariance across informants is
not explicitly tested, parent-adolescent discrepancies may reflect informant differences in
understanding the meaning of a construct (Vandenberg & Lance, 2000). Although both these
issues are remediable, two other limitations pose more serious threats to the validity of ODS.
First, because both individual scores have equal weight in the difference score, using ODS
relies on the untested assumption that effects of both informants’ reports on associated
variables also are equally strong (Edwards, 2002; Laird & De Los Reyes, 2013). Second,
subtracting two scores from one another reduces two scores to one, and as such, actual
discrepancy effects are confounded with the main effects of both informants’ scores (Edwards,
2002). Based on these issues, researchers have concluded that ODS “do not provide valid
tests of the utility of informant discrepancies” (Laird & De Los Reyes, 2013, p. 1), and several
researchers now advocate against their use (Laird & De Los Reyes, 2013; Scalas, Marsh,
Morin, & Nagengast, 2014).
In response to the critique on the ODS approach, the PRA approach has recently been
proposed as an alternative for studying informant discrepancies (Laird & De Los Reyes,
2013). PRA comprise regression analyses with higher-order terms included, such as quadratic
effects of, and interaction terms between different informants’ reports. Interaction terms
between informant reports are included to examine the extent to which informant
discrepancies affect outcome variables, in addition to the effects of both individual reports
(Laird & De Los Reyes, 2013; Edwards, 2002). Because the impact of both informants’
reports is empirically estimated, they can have different weight on associated variables.
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 6
Moreover, in PRA, discrepancy effects are not confounded with the main effects of both
informants’ scores. Despite these advantages, the types of research questions that can be
(simultaneously) addressed with PRA is rather limited. For example, using PRA does not
allow for examining how informant discrepancies of multiple dyads are interrelated and
together affect outcome variables, whether third variables affect the extent to which
informants disagree, or whether third variables moderate associations between informant
discrepancies and outcome variables.
A Flexible Alternative: Latent Difference Scores
In the current study, we propose a more flexible approach, Latent Difference Score
(LDS) modeling, to examine informant discrepancies. The LDS approach to informant
discrepancies was adapted from similar approaches from various disciplines, including social
psychology (Scalas et al., 2014), and developmental psychology (McArdle, 2009). In the case
of informant discrepancies, LDS models use second-order latent factors to examine
differences between different informants’ perceptions of the same behavior (e.g., self-rating
versus other-rating). First, latent factors representing individual informant reports are created
from observed item scores. Then, LDS (Δ) are created as second-order latent factors from the
latent factors representing individual informant reports, as:
Yother-rating = 1*Yself-rating + 1*Δself,other
By constraining the factor loadings of Yself-rating and Δself,other to be equal to 1, the results
of a subtraction are simulated, and the discrepancy score represents “the part of the score of
Yother-rating that is not identical to Yself-rating” (adapted from McArdle, 2009; p. 583). As such, the
discrepancy score provides information about differences in perceptions within a dyad, while
the effect of the self-rating is also taken into account. Discrepancy scores contain means (µΔ),
variances (σ2Δ), and a covariance with the self-rating (σΔ-self). When specified in this manner,
LDS represent directional difference scores; positive LDS means reflect higher other-ratings
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 7
compared to self-ratings, and negative LDS means reflect lower other-ratings compared to
self-ratings. Figure 1 shows a graphical presentation of a univariate LDS model; an Mplus
syntax for an example LDS model is provided as online supplementary material (Appendix
A).
>> INSERT FIGURE 1 ABOUT HERE <<
The LDS approach has several advantages over the ODS approach. First, LDS result
in the construction of two latent variables that represent the common (or identical) part of the
two informants’ scores, and the unique part of one of the informant’s scores (i.e., the part that
is not identical to the other informant’s score). As a result, effects of the discrepancy score
and one informant’s score on associated variables are not forced to be equal but rather, can be
empirically weighted within the model. Moreover, because one informant, and the
discrepancy score both are related to other variables, LDS do not confound the discrepancy
and main effects the way ODS do. Further, measurement errors of the associated constructs
can be partialled out, and it is possible to test for measurement invariance using LDS (Scalas
et al., 2014).
In contrast to the PRA approach, the LDS approach allows for the simultaneous
examination of several aspects of informant discrepancies, and for testing more complex
hypotheses. For example, the extent to which informants disagree (mean LDS), the extent to
which different dyads within a sample differ in the extent to which they disagree (variance
LDS), and correlates of informant discrepancies can all be studied simultaneously. Further,
LDS can be used as predictors, (concurrent) correlates, and outcome measures, all within one
model. Using LDS further allows for testing moderation of associations between informant
discrepancies and associated variables, and of changes in discrepancies over time. The LDS
approach thus is a highly flexible approach to studying informant discrepancies.
Empirical Illustration: Parent-Adolescent Discrepancies and Externalizing Problems
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 8
To empirically illustrate the LDS approach, interrelations between mother-adolescent
and father-adolescent discrepant views of parenting are examined, and their simultaneous
associations with concurrent and later adolescent adjustment problems are investigated. To
further demonstrate (some of) the types of research questions that can be addressed,
adolescent age and gender differences in the degree to which parent-adolescent dyads
disagree, and moderation of associations between the parenting factors and child adjustment
problems are explored. Parent-adolescent discrepant views of parenting were chosen because
discrepancies may be particularly pronounced for parents’ and children’s views of parenting
behaviors in early adolescence. During early adolescence, family relationships undergo
pronounced changes, as children spend more time unsupervised from parents, parent-child
communication decreases, and children strive for increasing autonomy from their parents
(Smetana, Campione-Barr, & Metzger, 2006; Steinberg & Morris, 2001). These changes in
family relationships may be associated with parent-child disagreement about parenting
behaviors. A certain amount of parent-adolescent disagreement is thought to serve key
developmental functions, such as the realignment of family relationships (Holmbeck &
O’Donnell, 1991; Steinberg & Morris, 2001) and adolescents’ striving for autonomy from
parents (McElhany et al., 2009). Conversely however, parent-adolescent disagreements may
reflect underlying problems that contribute to child psychopathology, such as family conflict,
poor communication, or lack of insight (Korelitz & Garber, 2016; Ohannessian & De Los
Reyes, 2014). A recent meta-analysis found parent-child discrepancies for a range of
parenting behaviors; generally, parents were found to view their own parenting more
favorably than children viewed their parents’ behaviors (Korelitz & Garber, 2016)
Most studies examining parent-child discrepant perceptions of parenting have used the
ODS approach (De Los Reyes, Goodman, Kliewer, & Reid-Quiñones, 2010; Gaylord et al,
2003; Guion et al., 2009; Maurizi, Gershoff, & Aber, 2012; OHannessian, 2012; Pelton &
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 9
Forehand, 2001; Pelton, Steele, Chance, & Forehand, 2001). Some studies have employed the
PRA approach, and found initial, although mixed, evidence of associations between parent-
child discrepancies and adolescent adjustment problems (Abar, Jackson, Colby, & Barnett,
2015; Laird & De Los Reyes, 2013; Ohannessian & De Los Reyes, 2014; Reidler & Swenson,
2012). In the current study, results from the LDS approach are compared to results obtained
using the two existing approaches, ODS and PRA.
Aims of the Current Study
The first aim of this study is to demonstrate, using an empirical example, how LDS
models are specified and how their results should be interpreted. It is therefore examined to
what extent mother-adolescent dyads and father-adolescent dyads disagree about a large
number of parenting behaviors, to what extent mother-adolescent and father-adolescent
discrepancies are interrelated, and whether parenting discrepancies differ according to
adolescent age or gender. Then, using hybrid models, associations between mother-adolescent
and father-adolescent discrepancies, and concurrent and later adolescent aggressive and rule-
breaking behaviors are examined. To illustrate the flexibility of this approach, moderation of
associations between the parenting factors and adolescent adjustment problems by adolescent
age and gender is further explored. The second aim of this study is to provide comprehensive
knowledge about the comparability of results obtained by the LDS approach and the other two
approaches for studying informant discrepancies. Therefore, associations between parent-
adolescent discrepancies and adolescent adjustment problems that are found using the LDS
approach are compared to results obtained from ODS and PRA.
Method
Procedure and Participants
This study is part of the longitudinal Flemish Study on Parenting, Personality, and
Development (FSPPD), which started in 1999 (Prinzie et al., 2003). In 1999, a proportional
stratified sample of elementary-school-aged children attending regular schools was randomly
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 10
selected. Strata were constructed according to geographical location, sex, and age.
Participants took part voluntarily, and anonymity and confidentiality were guaranteed. All
participants gave written informed consent. This study was conducted in full compliance with
pertinent international treaties, national laws, regulations, and codes concerning research
involving minors (children), as well as privacy. The study protocol meets the requirements of
the codes of conduct of pertinent professional associations, in particular of national and
international psychological and behavioral associations. Given that neither interventions nor
invasive actions were part of this study, the board of the Catholic University Leuven
(Belgium) approved this study, and in conformity with Belgian law, no further approval was
needed. Recruitment procedures are described more extensively in Prinzie and colleagues
(2003). For the current study, we used data that was collected at the beginning of adolescence
(Time 1), which corresponded to the 2007 wave. At Time 1, 477 adolescents, 470 mothers and
440 fathers provided information about mothers’ and fathers’ parenting behaviors. All
participants had the Belgian nationality. In 2007, adolescents’ ages ranged between 12 and 15
years (M = 13 years 6 months) and 52% (N = 248) were girls. Mothers’ age ranged between
39 and 64 years (M = 48 years 7 months), fathers’ ages ranged between 40 and 72 years (M =
47 years 7 months. At Time 2 (2009), 430 adolescents reported about their own adjustment
problems.
Measures
Parenting behaviors. In 2007, four reports on a large number of parenting
instruments were collected: mother self-report (MM); father self-report (FF); adolescent
report of mother’s parenting (AM), and; adolescent reports of father’s parenting (AF). The
different informant reports were equivalent in content, but wording of items was adjusted
slightly for each informant. All these instruments were included in the current study: the
Parenting Scale, overreactive discipline, and lax discipline subscales (PS; Arnold, O’Leary,
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 11
Wolff, & Acker, 1993; Prinzie, Onghena, & Hellinckx, 2007); the EMBU-C/P, (Egna Minnen
Beträffande Uppfostran-Child/Parent), overprotective control subscale (Deković et al., 2006;
Perris, Jacobsson, Lindström, von Knorring, & Perris, 1980); the Parenting Practices
Questionnaire, warmth/involvement and reasoning/induction subscales (PPQ; Robinson,
Mandleco, Olsen, & Hart, 1995), and; the Mother-Father-Peer-scale-33, autonomy granting
subscale (MFP-33; Epstein, 1983). The PS uses hypothetical discipline encounters followed
by two options, which act as opposite anchor points for a seven-point scale where 1 indicates
a high probability of using an effective discipline strategy (e.g.: “When I misbehave…” “My
mother speaks to me calmly”) and 7 indicates a high probability of making a discipline
mistake (“My mother raises her voice or yells”). The EMBU-C/P has four-point scale items,
ranging from 1 = no, never to 4 = yes, almost always. The PPQ comprises five-point scale
items, ranging from 1 = never to 5 = always. The MFP-33 uses four-point scale items, ranging
from 1 = entirely untrue to 4 = entirely true. Because each instrument uses different
answering formats, parenting factors were derived from each instrument separately, rather
than across instruments.
Parenting factors were empirically derived in two steps. First, dimensionality of the
constructs was assessed using Item-level Exploratory Factor Analyses across informants.
Results of these analyses indicate that all items of the a priori scale of reasoning (PPQ) loaded
on equivalent factors across informants. The empirical factors of warmth (PPQ), overreactive
discipline (PS), lax discipline (PS), and autonomy granting (MFP-33) contained 1-3 fewer
items than their a priori scales. The overprotective control scale (EMBU-C/P) broke up into
two empirical factors of three items each (Supplementary online material, Appendix B).
Measurement invariance of these factors across all four informants (AM; AF; MM;
FF) was assessed by comparing increasingly stringent models, reflecting (A) configural, (B)
metric, (C) scalar, and (D) full uniqueness invariance (Van de Schoot, Lugtig, & Hox, 2012).
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 12
For the PS and PPQ, models were analyzed using MLR estimation, for the EMBU-C/P and
MFP-33, models A-C were analyzed using the Theta parametrization and the WLSMV
estimator. If imposing invariance constraints resulted in a significant increase in the Satorra-
Bentler scaled Chi-square value and, additionally, in ΔCFI > -.01 supplemented by ΔRMSEA > .
015, or ΔSRMR > .03 (item loadings) or ΔSRMR > 0.010 (item intercepts, residual variances), the
respective constraint was not tenable (Chen, 2007). In all models, residual variances of
parallel items across informants were allowed to correlate (Marsh & Hau, 1996). Results
show that scalar invariance held for all factors of the PS, the PPQ, and the MFP-33
(Supplementary online material, Appendix C). It was, however, necessary to freely estimate
intercepts of some observed indicators for overreactive discipline and warmth. The empirical
factors of the EMBU-C/P were excluded from further analyses, because of several empirical
and interpretive difficulties with both factors.
Adjustment problems. Adolescents rated their own aggressive and rule-breaking
behaviors at T1 and T2 using the Dutch translation of the Youth Self-Report (YSR;
Achenbach, 1991; Verhulst, Van der Ende, & Koot, 1997). Extensive research has shown that
YSR test scores are reliable and that YSR test scores can be validly interpreted (Vignoe,
Bérubé, & Achenbach, 2000). Aggressive behaviors are rated using 17 items (e.g., “I fight a
lot”), and rule-breaking behavior are assessed using 15 items (e.g, “I steal from home”). Each
item is rated as 0 = not true, 1 = somewhat/sometimes true, or 2 = very/often true. In this
study, Cronbach’s αs for the aggressive and rule-breaking scales across measurement
occasions ranged between .81 and .89. Additionally, teacher-ratings of adolescent aggressive
and rule-breaking behaviors using the Teacher Report Form were used (TRF; Achenbach,
1991). At T1, correlations between adolescent-reports and teacher-reports (N = 419) of
aggressive and rule-breaking behaviors were r = .08, ns, and r = .23, p < .001, respectively. At
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 13
T2, correlations between adolescent-reports and teacher-reports (N = 282) were for
aggression, r = .19, p < .01, and rule-breaking, r = .53, p < .001.
Analytic strategy. In the first step of the analyses, multivariate LDS models in which
parenting factors regarding mothers and fathers were included simultaneously, were specified
to examine the extent to which (a) mother-adolescent and father-adolescent dyads disagree on
the parenting behaviors, and (b) parent-adolescent discrepancies are associated with parents’
self-reported parenting as well as with the other dyad’s perceptions of parenting (both self-
reported parenting and parent-adolescent discrepancy). Because covariates can be included in
these models, child age and gender differences in the parenting factors could also be
investigated. For model identification purposes, means of mothers’ self-reported parenting
behaviors, and means of child reports of mothers’ and fathers’ parenting were set to zero, and
factor loadings of the first observed indicator was set to one for each informant.
Then, the extent to which the parenting factors were associated with adjustment
problems was examined, and moderation of associations by child age and gender was
explored. For each parenting factor, models were specified for mothers and fathers, and for
concurrent and later adolescent aggressive and rule-breaking behaviors simultaneously. In
these hybrid models, child age and gender were included as covariates of the parenting
factors, and of children’s adjustment problems. Because LDS allows for testing moderation
effects, it could further be explored whether associations between the parenting factors and
children’s adjustment problems differed across child gender or age. To examine moderation
effects, both problem behaviors assessed at T2 were regressed simultaneously on interaction
terms between each mother-adolescent or father-adolescent LDS, and child gender or age
(centered). Given the exploratory nature and considerable number (20) of tests for
moderation, interaction effects were considered to be significant at p < .01.
Subsequently, associations between parent-adolescent discrepancies and adolescent
adjustment problems were investigated using the two known approaches for studying
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 14
informant discrepancies, ODS and PRA. For both these approaches, parenting factors were
computed that were identical to the empirically derived latent parenting factors. Thus, the
same items were used for the creation of all four informant reports (PRA), as well as the
discrepancy scores (ODS), as in the LDS part of the analyses. In the ODS analyses, all four
scores (self-report mothers; self-report fathers; mother-adolescent discrepancies; father-
adolescent discrepancies) were simultaneously related to adolescent externalizing problems,
using the same model specifications as in the analyses for the LDS factors. For the PRA
analyses, interaction terms between informant reports (reflecting parent-child similarity) and
quadratic terms were created in SPSS 23 and subsequently used in MPlus, given that
including multiple latent interaction terms simultaneously in MPlus is computationally highly
demanding. All analyses were conducted in MPlus 7 (Muthén & Muthén, 1998-2012)
Results
Parent-adolescent discrepancies: LDS Models. Model fit and model parameters of
the multivariate LDS models, in which mothers’ and fathers’ parenting behaviors were
included simultaneously, are shown in Table 1 (model fit indices, factor means and variances).
Comparison of the 95% confidence intervals of the LDS means indicate that on average,
adolescents rated mothers but not fathers higher on overreactive discipline and lax discipline
(positive LDS means). Further, adolescents rated both mothers and fathers lower on warmth
and reasoning than parents themselves (negative LDS means). Additionally, adolescents rated
fathers but not mothers lower on autonomy granting than fathers themselves. Significant
variances of all LDS indicate that there were significant differences between dyads in this
sample, regarding how much adolescents and parents differed in their views. Comparison of
the 95% confidence intervals for the means of the LDS of mother-adolescent versus father-
adolescent dyads further suggests that fathers and adolescents on average differed more in
ratings of warmth than mothers and adolescents did. Mother-adolescent and father-adolescent
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 15
dyads had similarly large discrepant views of overreactive discipline, lax discipline,
reasoning, and autonomy granting.
Negative correlations between parents’ self-reported parenting and the corresponding
LDS were found for all factors, and ranged between, r = -.17, p <.01 for maternal warmth,
and, r = -.59, p < .001 for maternal autonomy granting. The negative sign of the correlation,
together with the sign of the LDS mean (below/above zero), suggest that adolescents tended
to overrate mothers’ and fathers’ negative parenting behaviors (overrreactive discipline, lax
discipline) less if parents rated themselves higher on these behaviors, and adolescents tended
to underrate parents’ positive parenting behaviors (warmth, reasoning, autonomy granting)
more if parents rated themselves higher on these behaviors.
Further, correlations between mothers’ and fathers’ self-reported parenting behaviors
ranged from r = .17, p < .001 for warmth, to r = .32, p < .001 for autonomy; correlations
between mother-adolescent and father-adolescent discrepant perceptions ranged from r = .18,
p < .01 for overreactive discipline to r = .45, p < .001 for warmth. Thus, larger mother-child
discrepancies of all parenting variables were related to larger father-child discrepancies. Only
father self-reports on autonomy granting were related to smaller mother-child discrepancies
for this behavior, r = -.14, p < .05. All other paternal self-reports were unrelated to mother-
child discrepancies, and conversely, mothers’ self-reported parenting behaviors were all
unrelated to father-adolescent discrepancies.
Child age and gender differences in the parenting factors. Then, child age and
gender differences in parent-adolescent discrepant perceptions were examined (full results can
be obtained from the first author upon request). Results indicate that older adolescents
overrated mothers’ (b = 0.11, S.E. = 0.04, p < .05) and fathers’ (b = 0.17, S.E. = 0.05, p < .05)
overreactive discipline more than younger adolescents. Older adolescents underrated mothers’
(b = -0.13, S.E. = 0.03, p < .001) and fathers’ (b = -0.11, S.E. = 0.04, p < .01) warmth more,
and older adolescents underrated mothers’ reasoning (b = -0.11, S.E. = 0.03, p < .01) and
autonomy granting (b = -0.20, S.E. = 0.08, p < .01) more. Further, daughters of mothers
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 16
underrated mothers’ reasoning more than sons of mothers (b = -0.23, S.E. = 0.09, p < .01); no
other child gender differences in mother-child or father-child discrepancies were found.
Regaring parents’ self-reported parenting behaviors, mothers (b = -0.19, S.E. = 0.09, p < .05)
and fathers (b = -0.18, S.E. = 0.09, p < .05) of girls rated themselves lower on overreactive
discipline than parents of boys, and mothers of girls rated themselves higher on autonomy
granting than mothers of boys (b = 0.40, S.E. = 0.17, p < .05). Fathers of older children rated
themselves lower on warmth (b = -0.08, S.E. = 0.03, p < .05); no other child age effects on
parents’ self-rated parenting were found. In all hybrid models, child age and gender
differences in the parenting factors were taken into account by including these background
variables as covariates.
Discrepancies and adjustment problems: LDS approach. Hybrid models, in which
mothers’ and fathers’ self-reported parenting and mother-adolescent and father-adolescent
discrepancies were related to concurrent and later aggressive and rule-breaking behaviors,
showed adequate to excellent fit to the data. CFI values ranged between 0.91 for warmth to
0.98 for autonomy granting; RMSEA values ranged between .044 for reasoning and .027 for
autonomy granting (results not shown in a Table). Several parent-adolescent discrepancies
were concurrently correlated with aggressive and/or rule-breaking behaviors (Table 2).
Moreover, all concurrent correlations were in the expected direction. Specifically, stronger
mother-adolescent discrepancies of warmth and reasoning (i.e., more adolescent
underreporting) were concurrently related to higher aggressive and rule-breaking behaviors.
Further, stronger mother-adolescent and father-adolescent discrepancies of laxness (i.e., more
adolescent overreporting) were related to more rule-breaking behaviors. Additionally, stronger
father-adolescent discrepancies of overreactive discipline were related to more concurrent
aggressive behaviors. Mother-adolescent and father-adolescent discrepancies for autonomy
granting were all unrelated to concurrent aggressive and rule-breaking behaviors.
Additionally, only one (out of 20) longitudinal relation between parent-adolescent
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 17
discrepancies and adolescent externalizing problems was significant. Specifically, stronger
father-adolescent discrepancies on laxness were associated with relatively less aggressive
behaviors two years later1,2,3.
Then, moderation of associations between the parenting factors and adolescent
adjustment problems and adolescent age or gender were explored. None of the interaction
effects between the LDS and adolescent age or gender was significant at p < .01 (results can
be obtained from the first author upon request). Associations between the LDS and adolescent
aggressive and rule-breaking behaviors are thus similar (not significantly different) for
younger versus older adolescents or for boys versus girls.
Discrepancies and adjustment problems: ODS and PRA approaches. Comparison
of standardized beta-coefficients across approaches (Table 3) indicate that several associations
between two parenting factors and concurrent adjustment problems were statistically
significant across all three approaches. First, stronger mother-adolescent discrepancies in
warmth (i.e., more adolescent underreporting) were consistently associated with higher
concurrent adolescent rule-breaking behaviors and, second, stronger mother-adolescent
discrepancies in reasoning (i.e., more adolescent underreporting) were consistently associated
with higher concurrent adolescent aggressive behaviors.
Five concurrent associations were found to be significant in the LDS and ODS
approaches, but were not significant, and substantially smaller in the PRA approach. In both
discrepancy approaches, stronger father-child discrepancies in overreactive discipline, and
stronger mother-child discrepancies in warmth were concurrently related with more
aggressive behaviors. Further, stronger mother-child discrepancies in laxness and reasoning,
and stronger father-child discrepancies in laxness were concurrently associated with higher
rule-breaking behaviors.
Two associations between parent-adolescent discrepancies and concurrent adjustment
problems were found to be significant in the ODS approach, but not in the LDS or PRA
approaches, although sizes of the standardized beta coefficients were very similar between the
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 18
two discrepancy approaches. In the ODS approach only, stronger mother-adolescent
discrepancies were concurrently associated with more aggression, and stronger father-
adolescent discrepancies in warmth were associated with more rule-breaking behaviors.
Regarding longitudinal associations, one association was significant only in the LDS
approach, one other association was significant only in the ODS approach, and yet another
association was significant only in the PRA. Specifically, only in the LDS approach, stronger
father-child discrepancies in laxness were associated with less aggression two years later;
only in the ODS approach, stronger mother-adolescent discrepancies in overreactive
discipline were associated with more aggression, and; only in the PRA approach, stronger
mother-child similarity for overreactive discipline was associated with more aggressive
behaviors two years later. Given the number of estimated associations, and the inconsistency
in results across approaches, the longitudinal associations should be interpreted with caution.
All other concurrent and longitudinal associations were consistently non-significant, and
similar in size across approaches. To summarize, across approaches (LDS; ODS; PRA),
several parent-adolescent discrepancies were concurrently related to higher aggressive and
rule-breaking behaviors, but only very few longitudinal associations were found to be
significant. Moreover, the two discrepancy approaches yielded more similar results than the
PRA versus discrepancy approaches.
Discussion
Informant discrepancies of parallel and identical measures of the same construct are
ubiqutious, and can have substantive meaning in and of themselves. Existing approaches to
studying informant discrepancies are either limited by methodological issues, or have
restricted capability for the types of research questions that can be addressed. The current
study proposes an alternative, flexible approach to examining informant discrepancies, Latent
Difference Score (LDS) modeling (cfr., McArdle, 2009; Scalas et al., 2014). Moreover, results
obtained using the LDS approach were compared to results obtained using the two existing
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 19
approaches for studying informant discrepancies: Observed Difference Scores (ODS; see De
Los Reyes & Kazdin, 2004) and Polynomial Regression Analsyes (PRA; Laird & De Los
Reyes, 2011). As such, the current study provides comprehensive knowledge about the
comparability of the different approaches to studying informant discrepancies.
Parent-adolescent discrepant views. With the LDS approach, it was shown that
parent-child dyads differ in their ratings on a substantive number of parenting behaviors.
Because the constructs were assessed using invariance constraints across all four informants,
we can be confident that parent-adolescent discrepancies reflect true differences in
perceptions across informants, rather than being a statistical artefact. Although the intercepts
and residual variances of some indicators differed across informants, these were only few in
number and are unlikely to substantially affect results (Clark et al., 2016). Moreover, given
that the non-invariance was explicitly modeled in the LDS and hybrid models, its potentially
deleterious effects were likely lessened (Edwards & Wirth, 2009). Generally, parents rated
themselves more favorably than adolescents rated their parents, consistent with a recent meta-
analysis on parent-child discrepant perceptions of parenting (Korelitz & Garber, 2016), and
there were several effects of child age and parental gender on parent-child discrepancies. The
pattern of results suggests that social desirability may drive parents to give consistently more
favorable ratings of their own behaviors than adolescents do, and are indicative of parents’
aspirations to meet the social norm of being “a good parent” (Janssens et al., 2015).
Conversely, adolescents may view parents’ behaviors overly negative because they have a
“developmental stake” in achieving autonomy and minimizing emotional closeness with their
parents (Bengston & Kupers, 1971; Korelitz & Garber, 2016). Adolescents may therefore
rebel against, or individuate from their parents’ views (Smetana, Campione-Barr, & Metzger,
2006; Steinberg & Morris, 2001), resulting in them overrating negative types of parenting,
and underrating positive types of parenting.
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 20
Very few child gender differences were found for parent-child discrepancies, but there
were several parental gender differences. Thus, whereas children’s gender does not seem to
affect how much parents and their children disagree about parenting, parental gender may
affect the specific types of parenting that dyads disagree about. Mother-child dyads differed in
perceptions of mothers’ ineffective (overreactive, lax) discipline, but father-child dyads
differed in perceptions of fathers’ autonomy granting; both mother-child and father-child
dyads differed in perceptions of warmth and reasoning. The finding that adolescents disagreed
with their mothers about ineffective discipline strategies, could reflect the fact that the social
pressure to be a ‘good parent’ is stronger for mothers than fathers, as intensive mothering
continues to be the predominant ideology in western society. As such, mothers may be even
more inclined than fathers to answer questions about ineffective parenting strategies in a
socially desirable way. Further, society still expects mothers to have greater responsibility for
parenting than fathers do (Arendell, 2000; Moon & Hoffman, 2008). The finding that
adolescents’ and fathers’, but not adolescents’ and mothers’, views of autonomy support
diverged, may reflect that fathers are more responsible for setting limits outside the family
home, whereas mothers are more responsible for rules inside the family home (Eagly &
Johannesen-Schmidt, 2001). Perceptions of warmth and reasoning differed between mothers
and adolescents, and fathers and adolescents. These two types of parenting behaviors are
closely related to the parent-child relationship quality, which is known to decrease during
early adolescence (e.g., Smetana et al., 2006). These findings are further in line with existing
work showing that there is a temporary increase in family conflict during the early adolescent
years (see, Eccles et al., 1993). Parent-adolescent disagreement about these two types of
parenting behaviors may thus reflect a temporary decrease in parent-child relationship quality,
which may ultimately drive the realignment of family relationships in early adolescence
(Holmbeck & O’Donnell, 1991; Steinberg, 1991; Steinberg & Morris, 2001).
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 21
Consistent with results from a meta-analysis on correspondence in parent-child dyads
regarding parenting (Korelitz & Garber, 2016), older adolescents disagreed more with their
parents than younger adolescents on several parenting behaviors, but very few differences
were found between parent-son versus parent-daughter dyads. Parent-child dyads with older
children may be less close, with older adolescents having gained more autonomy from their
parents and spending more time unsupervised by their parents, which may in turn cause
parents and children to diverge more on perceptions of parenting behaviors as children grow
older. Because the LDS approach allows for examining repeatedly measured informant
discrepancies, future longitudinal research could examine (true) developmental changes in
parent-child discrepancies of parenting during early adolescence as well as in other
developmental phases.
Within families, mother-adolescent discrepancies were consistently related to father-
adolescent discrepancies. Because adolescents are in both dyads, these relations between
mother-adolescent and father-adolescent dyads are of course at least in part due to same-rater
bias. On a substantive level, these results may reflect differences between families in the level
and quality of communication; in families wherein the quantity or quality of communication
between parents and children is lower, discrepant views are likely more prevalent (De Los
Reyes & Kazdin, 2005; Treutler & Epkins, 2003). In addition to these family-level factors,
individual child and parental characteristics such as personality or psychopathology may
affect the extent to which adolescents and their mothers and fathers differ in their views (De
Los Reyes, Goodman, Kliewer, & Reid-Quinones, 2008; Korelitz & Garber, 2016). Because
LDS can be used as a predictor and outcome variable in the same model, using LDS allows
for an examination of whether parent-child discrepant views indeed explain (mediate)
associations between predictor variables and outcomes. Future research that includes multiple
types of predictors can provide comprehensive knowledge about the factors that affect the
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 22
extent to which adolescent-mother and adolescent-father dyads differ in their views of
parenting.
Parent-adolescent discrepancies and adjustment problems across approaches.
Regardless of the analytic approach (LDS, ODS, PRA), several parent-adolescent
discrepancies were concurrently related to higher aggressive and rule-breaking behaviors, but
only very few longitudinal associations were found to be significant. This pattern of findings
is supportive of the notion that parent-adolescent disagreement reflects underlying problems
that contribute to child psychopathology, such as family conflict, poor communication, or lack
of insight (Guion et al., 2009; Ohannessian & De Los Reyes, 2014), but in the short term only.
Nevertheless, because adjustment problems are known to be persistent (Dishion & Patterson,
2006), parent-child disagreement regarding parenting behaviors may still have substantive
long-term consequences for adolescents, above and beyond parents’ ‘actual’ parenting
behaviors. Conversely, however, these results may suggest that adjustment problems are the
cause of, rather than the result of parent-adolescent discrepancies, consistent with ideas that
psychopathology affects one’s perceptions of behavior (Barker, Bornstein, Putnick,
Hendricks, & Suwalsky, 2007; De Los Reyes et al., 2008; Korelitz & Garber, 2016). Research
that utilizes a repeated-measures design, in which informant perceptions of parenting and
adjustment problems are assessed repeatedly is necessary to provide knowledge about the
direction of effects between parent-adolescent discrepancies and adolescent externalizing
behaviors. The LDS approach allows for investigating repeated measures of informant
discrepancies, thus providing a much-needed opportunity for examining direction of effects
between parent-child discrepancies and children’s adjustment problems specifically, and
informant discrepancies and associated constructs more generally.
Across approaches, stronger mother-child discrepancies of warmth were associated
with more concurrent rule-breaking behaviors, and stronger mother-child discrepancies of
reasoning were associated with more aggression. In both discrepancy score approaches, but
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 23
not in the polynomial regression analyses, stronger mother-child discrepancies of warmth
were additionally related with more aggressive behaviors, and stronger mother-child
discrepancies of reasoning were also associated with more rule-breaking behaviors. Further,
stronger mother-child and father-child discrepancies of lax discipline were associated with
more concurrent rule-breaking behaviors, and stronger father-child discrepancies of
overreactive discipline were associated with more aggressive behaviors. Parent-adolescent
discrepant views of autonomy granting were, however, not associated with adjustment
problems. Overall, mother-child discrepancies were thus associated more often with
adjustment problems than father-child discrepancies. This difference in results for mothers
versus fathers may be because gender roles, which expect women to act in a caring and
nurturing fashion and to be the main caregiver, whereas men are expected to take on more
agentic roles (Eagly & Johannesen-Schmidt, 2001).
Overall, only very few (two) concurrent associations between interaction terms created
from informant reports of parenting and adolescent adjustment problems were significant in
the PRA, much less than found in the LDS and ODS approaches. This difference may be due
to the fact that, in the difference scores approaches, the adolescent report is taken into account
in the discrepancy (i.e., “the part of the adolescent score that is not identical to the parent
score”) whereas in the PRA approach, the effects of both informant reports are partialled out
from the similarity index (interaction term). Although it may appear that the PRA approach
provides a more stringent test of the extent to which informant discrepancies are associated
with outcome variables, it is important to note that interaction terms do not provide
knowledge about whether more under- or overreporting of a construct by one informant
versus the other is associated with other constructs, but rather, whether the effect one
informant’s report on an outcome variable is affected by the other informant’s report. These
results may also be due to a power issue in the PRA approach, which is reflected by the often
small sizes of interaction effects. Research that can compare the discrepancy and PRA
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 24
approaches using large samples will likely shed more light on the reasons underlying the
relative lack of significant interaction effects in the PRA approach, compared to the number of
significant associations found in the discrepancy approaches.
Comparison of associations between analyses using the LDS and ODS approaches
indicate that both types of analyses yield highly similar results, which is not surprising given
that in both approaches, discrepancy scores are similarly construed. Moreover, if ODS are
created from items that have been empirically demonstrated to be invariant across informants,
the increased unreliability of discrepancy scores thus do not necessarily result in downwardly
biased estimates. Other researchers have similarly argued that, when research aims to provide
knowledge about group-level processes, the standard interpretation of reliability does not
always hold and therefore, lower reliability may not substantively affect results (Thomas &
Zumbo, 2012). It should be noted, however, that the similarity in findings across the two
approaches in the current study do not necessarily generalize to other constructs. Moreover,
the LDS approach has several methodological and theoretical advantages compared to the
observed difference scores approach, such as not confounding both informant reports with the
discrepancy score, not assuming that both informants’ reports have equal effects on associated
variables, and taking into account the fact that the two informant reports may have different
variances (cfr. Laird & De Los Reyes, 2012).
Limitations and future research. This study provides valuable knowledge about
within-family processes of parent-adolescent discrepancies, and the effects of such
disagreements for adolescent functioning. Nevertheless, several limitations warrant caution in
the interpretation of results. Although in the current study, parent-adolescent discrepancies
were conceptualized as the difference between parental self-reports and adolescent reports of
parents, results cannot inform other research about which informant provides ‘better’
information of parenting because no ‘objective’ measures of parenting (e.g., observations),
were available to compare both informants’ reports with. Because additional analyses showed
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 25
that all models replicated well on teacher-reports of adolescent adjustment problems3, we are
confident that relations between parenting discrepancies and adolescent aggressive and rule-
breaking behaviors are not due to same-rater bias alone. Nevertheless, studies that include
other measures of parenting, such as observations of parent-child interactions, can yield
crucial knowledge about the validity and usefulness of both informants’ (parents and
adolescents) reports of parenting.
Several limitations specific to the LDS approach should also be noted. First, a
prerequisite for the LDS approach, and for all research examining informant discrepancies is
measurement invariance of the constructs across informants. Obtaining invariant constructs
allows researchers to make substantive conclusions about informant differences, whereas
failing to assess measurement invariance may lead to incorrect conclusions, as informant
differences may be due to statistical artefacts. However, achieving measurement invariance
can be very difficult. For example, because of statistical and interpretitive difficulties with the
factors derived from one instrument, the EMBU-C/P, these factors could not be used in further
analyses. At the other hand, the factors for warmth and reasoning strongly resembled the
original scales. Thus, although measurement invariance can be difficult to obtain, it may be
different for different types of instruments and constructs. Generally, researchers interested in
multi-informant data are strongly advised to make sure different informants apply the same
meaning to the underlying construct. Second, the specification of the LDS scores prohibits an
examination of the effects of both individual scores, in addition to the discrepancy score. The
polynomial regression analyses is better suited for examining questions of how both
informants affect an outcome, in addition to their discrepant perception. Third, the
interpretation of associations between the discrepancy scores and other variables can be
complex, given that the direction of the discrepancy (e.g., adolescent overreporting compared
to parents) has to be taken into account for a correct interpretation. Researchers should thus be
careful when interpreting their results.
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 26
Conclusions
The current study aimed to apply a flexible approach to examining parent-adolescent
discrepant perceptions, Latent Difference Score modeling. Further, this study demonstrated
the utility of this approach by examining how mother-adolescent and father-adolescent
discrepancies of a variety of parenting behaviors were interrelated, and together affect
concurrent and later adolescent aggressive and rule-breaking behaviors. Moreover, results
obtained from this approach were compared to results obtained by the two existing
approaches for studying informant discrepancies, Observed Difference Scores and Polynomial
Regression Analsyes. Parents and adolescents were found to differ in their perceptions of
most parenting behaviors, but the types of parenting that parent-child dyads disagreed on were
somewhat different for mothers versus fathers. Further, discrepancies were smaller in parent-
adolescent dyads in which parents rated themselves less favorably. Discrepant perceptions of
mother-adolescent and father-adolescent dyads were consistently interrelated. Moreover,
several parent-adolescent discrepancies were related to concurrent higher aggressive and rule-
breaking behaviors. Although most significant results generalized across the two discrepancy
approaches, only very few significant interaction terms were found in the polynomial
regression analyses. Overall, results suggest that parent-adolescent discrepancies are
ubiquitous, and are consistently related to higher adjustment problems in the short term.
Using Latent Difference Scores provides a flexible tool for examining several aspects of
informant discrepancies simultaneously.
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 27
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Footnotes
1. Coefficients obtained from the empirically derived parenting factors were compared from
analyses in which latent factors identical to the a priori scales were used. Four associations
were only significant for the a priori parenting factors, and conversely, four associations were
only significant for the empirically derived factors; nevertheless, sizes of these coefficients
were highly similar. We are therefore confident that the empirically derived factors closely
resemble their a priori scales.
2. It was explored whether associations between parent-adolescent discrepancies and
adjustment problems are moderated by the direction of the discrepancy (i.e., adolescent
overreporting versus underreporting, compared to parents). Because moderation by direction
of the discrepancy score cannot be modelled directly in MPlus, dummies were created from
saved factor scores for each LDS separately, reflecting dyads in which adolescents had more
negative versus more positive views of parenting, compared to parents themselves. It was
then examined whether correlation matrices differed for the two types of dyads, by comparing
model fit indices of matrices in which all correlations were estimated freely for adolescent
overreporters versus underreporters, to matrices in which correlations between the measures
of interest (i.e., parent-adolescent discrepancies, and adolescent aggressive and rule-breaking
behaviors) were constrained to be equal for adolescent overreporters versus underreporters.
Chi-square differences between the nested correlation matrices ranged between Δχ2 (4) = 0.47,
p = .98 for mother-adolescent discrepancies of autonomy, and Δχ2 (4) = 8.14, p = .09, for
mother-adolescent discrepancies of overreactive discipline. Associations between the LDS
and adolescent aggressive and rule-breaking behaviors are thus similar (not significantly
different) for dyads in which adolescents have more negative versus more positive views of
their parents’ parenting behaviors, compared to parents themselves.
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 34
3. It was explored whether associations can be replicated on teacher-reports of adolescent
aggressive and rule-breaking behaviors. Specifically, teacher-rated adolescent aggressive and
rule-breaking behaviors were added to the multivariate LDS models in which adolescent
adjustment problems were predicted from mothers’ and fathers’ self-rated parenting behaviors
and adolescent-mother, and adolescent-father discrepancies. Each of the models was analyzed
twice: once, associations between self-ratings versus teacher-ratings of externalizing
behaviors and all parenting constructs were freely estimated, and once, these were constrained
to be equal across teacher-ratings and adolescent-ratings. Although increments in chi-square
were significant for several models, relative fit indexes did not change substantially; all ΔCFI
< .006, ΔRMSEA < .002, and ΔSRMR < .007 (see supplementary online material, Appendix
D for all model comparisons). Associations between the parenting factors and teacher-rated
adjustment problems in the unconstrained models show that the parenting factors were
generally not significantly associated with teacher-rated adjustment problems (Supplementary
online material, Appendix E). Nevertheless, given that constraints across reporters did not
lead to appreciable changes in model fit, associations between the parenting factors could be
replicated on teacher-reports of adolescent aggressive and rule-breaking behaviors. We can
thus be confident that associations between parent-adolescent discrepancies, and aggressive
and rule-breaking behaviors are not due to same-reporter bias alone.
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 35
Table 1
Model Fit Indices, and Means and Variances of Mothers’ and Fathers’ Self-Reports and Parent-Child Latent Discrepancy Scores (LDS).
Model Fit Indices
Means Variances
Self-Report LDS Self-Report LDS
χ2df CFI RMSEA MM FF AM AF MM FF AM AF
Overreactive
discipline
458.66 235
0.91 .044 0.00a-0.06a0.19b0.06ab 0.73*** 0.71*** 0.77*** 1.07***
Lax discipline 593.59 334 0.91 .040 0.00a0.15b0.27b0.20b0.37*** 0.43*** 0.50*** 0.68***
Warmth 1349.32 723 0.92 .042 0.00a-0.45b-0.47b-0.65c0.31*** 0.37*** 0.46*** 0.85***
Reasoning 511.14 240 0.95 .048 0.00a-0.24b-0.43c-0.43c0.30*** 0.35*** 0.64*** 0.76***
Autonomy granting 341.03 258 0.98 .026 0.00a-0.13a-0.41ab -0.58b1.40*** 1.23*** 1.91*** 2.41***
Note: Latent means of mothers’ self-reported parenting behaviors were set to zero for identification of the model. Different superscripts indicate
significant mean-levels, indicated by non-overlapping 95% confidence intervals.
Table 2
Associations between Parents’ Self-reports, Parent-Child Discrepant Views, and Adjustment Problems.
Initial time-point
correlations
Longitudinal associations
Aggression Rule-breaking
Aggression Rule-break b SE β b SE β
Overreactive
SelfMother .28*** .22*** 0.76 0.22 .18** 0.27 0.17 .09
SelfFather .20** .16** 0.06 0.24 .02 0.001 0.19 .00
ΔMother,Child .05 .06 0.27 0.21 .07 0.09 0.15 .03
ΔFather,Child .15* .10 0.01 0.18 .01 0.01 0.15 .01
Laxness
SelfMother .08 .15*** 1.27 0.43 .18** 0.38 0.28 .08
SelfFather .07 .06 -0.11 0.33 -.02 0.20 0.28 .04
ΔMother,Child .11 .11* 0.51 0.41 .09 0.01 0.28 .003
ΔFather,Child .01 .14* -0.78 0.34 -.15* -0.37 0.25 -.10
Warmth
LATENT DIFFERENCE SCORES FOR DISCREPANCIES 36
SelfMother -.07 -.10 -0.21 0.44 -.03 -0.40 0.33 -.08
SelfFather -.20*** -.20*** 0.10 0.46 .02 0.54 0.30 .11
ΔMother,Child -.18** -.21*** -0.24 0.36 -.04 0.03 0.29 .01
ΔFather,Child -.10 -.10 0.23 0.29 .05 0.19 0.21 .06
Reasoning
SelfMother .03 .02 0.32 0.43 .04 0.18 0.30 .03
SelfFather -.09 -.06 0.61 0.42 .09 0.26 0.29 .05
ΔMother,Child -.13* -.20*** 0.15 0.37 .03 0.19 0.27 .05
ΔFather,Child -.01 -.08 0.58 0.32 .12 0.19 0.22 .05
Autonomy
SelfMother -.10* -.16** -0.51 0.41 -.10 -0.01 0.29 -.003
SelfFather -.12* -.11* 0.77 0.38 .14* 0.53 0.27 .14
ΔMother,Child -.02 -.03 -0.14 0.39 -.03 -0.04 0.30 -.01
ΔFather,Child -.04 -.06 0.62 0.33 .14 0.32 0.26 .10
Note: Results regarding within-time point correlations between all constructs, stability coefficients, and cross-lagged effects between aggressive and rule-
breaking behaviors can be obtained from the first author upon request. * p < .05. **p <.01. *** p < .001.
Table 3
Standardized Beta-coefficients (β) between Parent-Child Discrepant Views and Concurrent and Later Adjustment Problems:
Comparing Latent Difference Scores (LDS), Observed Difference Scores (ODS), and Polynomial Regression Analyses (PRA).
Initial time-point correlations Longitudinal associations
Aggression Rule-breaking Aggression Rule-breaking
LDS ODS PRA LDS ODS PRA LDS ODS PRA LD
S
ODS PRA
Overreactive discipline
Mother-Child .05 .04 .03 .06 .03 .003 .07 .09* .02 .03 .04 .11*
Father-Child .15* .14* -.05 .10 .07 .02 .01 -.02 .07 .01 -.02 .07
Lax discipline
Mother-Child .11 .09* -.04 .11* .11* -.01 .09 .05 -.00
3
.003 -.02 .001
Father-Child .01 .03 .01 .14* .13** .05 -.15* -.10 .02 -.10 -.06 .001
Warmth
Mother-Child -.18** -.17** -.07 -.21*** -.19*** -.09* -.04 -.02 .05 .01 .01 .02
Father-Child -.10 -.09 -.05 -.10 -.10* -.02 .05 .04 .02 .06 .06 -.00
1
Reasoning
Mother-Child -.13* -.12* -.15** -.20*** -.19*** -.06 .03 .05 -.03 .05 .07 .000
Father-Child .01 .004 .03 -.08 -.05 .03 .12 .08 .03 .05 .03 .01
Autonomy granting
Mother-Child -.02 -.02 -.02 -.03 -.04 .06 -.03 -.01 -.05 -.01 -.00
4
-.03
Father-Child -.04 .05 .03 -.06 -.09 .04 .14 .09 .01 .10 .09 -.04
Note: Main effects of parental self-reports (LDS; ODS), child reports (PRA), and higher-order effects of both informants’ reports
(PRA) were also estimated, but not shown for clarity of presentation.
* p < .05. **p <.01. *** p < .001.
FIGURE CAPTIONS
Figure 1. Graphical Presentation of a Univariate LDS Model for Informant Discrepancies.
LDS MODELS FOR DISCREPANT PERCEPTIONS 1
Note: Correlations between residual variances of same items across informants were also estimated, but not shown for clarity of
presentation. Constraints are indicated by similar labels for the factor loadings, error intercepts, and residual error variances.
Self-rating
Other-rating
Observed
Indicator 1
Δself,oth
er
a
1
1
µSelf
σSelf
Observed
Indicator 2
Observed
Indicator X
Observed
Indicator 1
Observed
Indicator 2
Observed
Indicator X
µΔself,
other
σΔself,
other
b
x
a
b
x
…
…
σ2Δ,self
e1
e2
ex
e1
e2
ex
µea
σea
µeb
σeb
µex
σex
µea
σea
µeb
σeb
µex
σex
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