Do Difference Scores Make a Difference on the Third-person Effect？

冯广超

Abstract：Researchers from different fields have been intrigued but also confused with regard to the ways of conceptualizing and operationalizing difference.This paper critically reviewed a number of existing means of operationalizing difference and mathematically explicated and empirically tested why difference scores were problematic and why the diamond model that aimed to replace difference scores was equally troublesome.Ultimately，this paper recommended polynomial regression as an alternative to difference scores.

Key words：third-person effect　difference score　reliability

The construct of difference is of persistent research interest across disciplines.For instance，in sociology，it has been widely applied in studies of status difference and mobility.In the management literature（for a review，see Peter，Churchill Jr，and Brown），difference has been used in addressing the job fit between a person and the environment，the similarity between perceptions，matches between personal values and organizations’cultures，and agreement in ratings，among other topics.In communication，it has also been an intensively researched area，particularly in studies of perceptual differences in the third-person effect（TPE）（Davison，1983）.

Third-person perception（TPP）predicts that people exposed to persuasive communication tend to see it as having a greater effect on others than on themselves，particularly when messages are presumed to have undesirable social consequences（Hoffner&Rehkoff，2011）.The behavioral component of the TPE often hypothesizes that people might act upon such perceptual disparities，which could lead them to support the regulation of undesirable messages（Hoffner&Rehkoff，2011；Sun，Shen，&Pan，2008）.The stronger the perceived harm of media messages is on others，the more likely people are to support restrictions.Traditionally，scholars have operationalized perceptual disparities by calculating the simple difference between the perceived effects on self and on others；then，the difference score worked as an independent variable for predicting the outcome variable，i.e.，support for censorship of messages.

There exist a number of proposals for addressing differences among disciplines.Methodologists and psychometricians have also expounded the fundamentals of operationalizing difference，and they offered solutions many years ago for obviating problems relative to measuring differences，but many applied scholars have simply ignored these developments and have repeated the problems in one way or another.This paper aims to bridge the gap among disciplines and particularly to elaborate on the problems and new developments with regard to methods of operationalizing differences.

Difference scores and problems thereof

The construct of difference was intuitively operationalized with various forms of mathematical differences，e.g.，the algebraic difference，the absolute difference，and the squared difference.Such methods of operationalizing difference are usually called difference scores.Although straightforward，they all suffer from similar limitations，e.g.，unfounded constraints and downgrading of reliability.That is，the different score placed some constraints on the TPE；these constraints were，in fact，never tested and hence are unfounded；the reliability of the difference score is not the simple average of the reliabilities of the two components，and it often decreases compared to the reliabilities of original component variables.Nevertheless，difference scores have long been used，and they remain popular across the social sciences.Therefore，these problems will be reviewed briefly below.Due to the similarities shared among the three types of difference scores，only the algebraic difference is illustrated as an example.

Untested constraints

Due to the popularity of the TPE in communication，we use it as a naave example in which the perceptual gap between the self and others is used to predict a behavior（e.g.，support for censorship of messages）.This relationship can be represented by the following equation：

where xs and x0 are the perceived effects on self and others，respectively.The expansion of Equation 1 yields：

The comparison between Equations 1 and 2 shows that using xs-xo as a predictor constrains the coefficients on xs and xo to be equal in magnitude but opposite in sign（i.e.，β1=-β2）.Edwards（2002）maintained that this restriction imposes untested constraints on the coefficients relating xs and xo to y and that this constraint should not be taken for granted but rather should be treated as a hypothesis to be tested.

Downgrade of reliability

According to classical test theory（Crocker&Algina，1986），the reliability coefficient is the ratio of the true score variance to the total variance of the observed measurement.The variance of an algebraic difference score is：

where COV is the covariance.As seen from Equation 3，σ2d is affected by not only the variances of original component measurements but also the covariance between them，which are sample dependent.Correspondingly，the formula for the reliability of an algebraic difference（see ENREF16 Guilford）is：

whereρdd′is the reliability of the difference score，ρxsx′s andρxox′o are the reliabilities of the self and others，respectively，andρxsxo is the correlation between the self and others.When the variances of the self and others are equal（i.e.，σ2xs=σ2xo），Equation（4）changes to：

Most applied researchers have further unwittingly assumed that the correlation between self and others was zero in Equation（5）.As a result，the reliability of difference scores is simply the average of the reliabilities of the self and others.These restrictive assumptions，i.e.，equal variance and a zero correlation，have nevertheless been rarely met in real studies.

In addition，if the reliabilities of the two component variables（i.e.，self and others）are equal，i.e.，ρxsx′s=ρxox′o，Equation（5）becomes：

Equations（5）and（6）demonstrate that the correlation between the components seems to be a nuisance affecting the reliability of difference scores.Many studies（e.g.，Chiou&Spreng，1996；Edwards，2001，2002）have revealed that，when component measurements are positively correlated，difference scores are less reliable than either component.However，if the correlation between the components is negative，the reliability of the difference score improves compared that of the components（Tisak&Smith，1994）.Altogether，unreliable difference scores are deemed to be detrimental，e.g.，with low discriminant validity and spurious correlations（Peter et al.，1993）.

Burt and Obradovi（2013），however，argued that criticisms of difference scores almost always have focused on situations in which the components themselves have equal numbers of both variances and reliabilities，which place an upper limit on the reliability of difference scores.Chiou and Spreng（1996）also found that the unequal standard deviations of the components can significantly improve the reliability of the difference score，especially when the correlation between the components is high（Peter et al.，1993）.Moreover，some studies（Burt&Obradovi，2013；D.Rogosa，Brandt，&Zimowski，1982；D.R.Rogosa&Willett，1983；Tisak&Smith，1994）have even defended the use of difference scores，particularly when the individual difference in true change is appreciable.

The validity problem

In addition to the reliability issue mentioned above，validity is another concern.That is，difference scores are incapable of measuring what they claim to measure because they confound the effects of the components of difference（Edwards，2002）.From Equations（1）and（2），it can be seen thatβ1 can reflect a positive relationship for xs，a negative relationship for xo，or some combination thereof.Some studies have attempted to address this confounder by controlling for the components of difference，which can be shown as：

The further expansion of Equation（7）yields：

As seen from Equation 8，β2 is not the effect of xs-xo but instead is the negative effect of xo，controlling for xs（Wall&Payne，1973）.If the other component is also added，the equation after expansion will be：

Peter et al.（1993），Schmierbach，Boyle，and McLeod（2008），and Eeckhaut，Van de Putte，Gerris，and Vermulst（2013）considered Equation（9）to be more troublesome because multicollinearity among the terms can produce unstable parameter estimates and misleading results.The more dramatic finding of Hendrickx，De Graaf，Lammers，and Ultee（1993）with regard to Equation（9）was that the difference score is a linear transformation of the two components，and such a model would therefore be unidentifiable.

Some earlier scholars（L.Cronbach，1955；L.J.Cronbach&Gleser，1953；Johns，1981）proposed profile similarity indices or PSIs（e.g.，the sum of absolute differences and the sum of squared differences）as alternatives to difference scores，but PSIs were believed to suffer from the problems of ambiguous conceptualization，loss of essential information，and the imposition of highly restrictive constraints on the coefficients，according to Edwards（1993）.

Means of operationalizing difference in TPE

The old practice

Previous studies examining the behavioral component of the TPE used the magnitude of difference in perceived effects on self and others as a predictor of support for media restrictions.However，the findings have been mixed（Perloff，1999）and even contradictory at worst（Boyle，McLeod，&Rojas，2008）.For instance，the magnitudes of perceptual bias were reported as significant predictors of support for restrictions on pornography（Gunther，1995；Rojas et al.，1996），sensitive TV content（Gunther&Ang，1996），rap music（McLeod et al.，1997），advertising（Shah，Faber，&Youn，1999），and political campaign messages（Salwen，1998；Price et al.，1998），but they failed to show any predictive power over the censoring of pornography（Lo&Paddon，1998），the coverage of the O.J.Simpson trial（Salwen&Driscoll，1997），and the external control of political communications（Rucinski&Salmon，1990）.

Various causes that might account for the mixed results have been speculated upon.Schmierbach et al.（2008）attributed them to methodological inconsistencies，and they reported four methods commonly used by researchers into the TPE（i.e.，the standard subtractive measurement，the diamond model，first-and third-person estimates entered separately，and the subtractive measurement，with self-estimates as a control）.Specifically，57 of 73 articles adopted a subtractive measurement（other minus self）or the simple difference score.In addition，among 19 articles that employed some alternative measurement tactics，three articles presented models in which the subtractive score and a measurement of effects on self were simultaneously entered，and four articles presented some form of the diamond model.A number of past studies（Gunther，1998；Lo&Wei，2002；Salwen，1998）have specifically questioned the use of difference scores to test the perceived media effects on behavioral outcomes.Schmierbach et al.（2008）held that the subtractive measurement of difference scores might mask the real influence on support for censorship and that it potentially confounds relative difference with the absolute level of the variables in question.Lo and Wei（2002）also suggested that the inconsistency was largely due to the inappropriate use of perceptual bias as a predictor.They argued that the magnitude of perceptual bias was inevitably related to perceived effects on self.Because perceived effects on self and the magnitude of perceptual bias are collinear variables，it is statistically difficult to determine their separate effects on support for pornography restrictions（Hamilton，1992；Neter，Wasserman，&Kutner，1983）.Lo and Wei（2002）thus concluded that the magnitude of perceptual bias was an unreliable predictor of support for restricting online pornography.

Acknowledging the problems associated with the use of difference scores，some studies have remedied this issue by adding either the presumed influence on others（e.g.，Gunther and Storey（2003）；Salwen（1998）；Hoffner et al.，1999）or the influence on self（Gunther，1995；B.Lee&Tamborini，2005；C.Lee&Yang，1996）.We might wonder why these studies did not add the perceived effects on both self and others at the same time.From Equation 9 reviewed above，we realize that to add either is completely driven by data，namely to find a significant effect（with either the name of TPE or other names）.

The diamond model

The problems of adopting the simple difference score have also been gradually noted in the field of communication.A new panacea seems to be the diamond model，which originated in sociology.Originally designed to investigate the status inconsistency and social mobility effects，the diamond model（Hope，1975）has gained currency in communications，particularly in studies of the TPE（e.g.，Boyle et al.，2008；Eveland，Nathanson，Detenber，&McLeod，1999；McLeod，Eveland，&Nathanson，1997；Neuwirth&Frederick，2002；Shah，Faber，&Youn，1999；Sun et al.，2008）.The equation of the diamond model is as follows：

It amends the model of difference scores by adding an additive term of the two components，dubbed“the second-person effects”（2PE）by Neuwirth and Frederick（2002）and“the powerful-media effect”by Sun et al.（2008）.Neuwirth and Frederick（2002）held that the additive term references the level of media influence on self and others（2PE），controlling for self-other differences（the TPE and the first-person-effect or FPE）.

The diamond model is rooted in the following two equations：

Hope（1975）posited that an inconsistency（difference）effect is demonstrated if Equation（10）explains significantly more variance in y than Equation（12）does.The diamond model is，unfortunately，problematic because Equation（10）explains exactly the same amount of variance of y as Equation（11）（Hendrickx et al.，1993；Schmierbach et al.，2008）.The diamond model（Equation（10））might be better than Equation（12），merely because Equation（12）forcesβ2 to be equal toβ1 in Equation（11）.The parsimony principle of statistics——which says that if two models are equal and competing，the simpler model should be chosen or that if a variable can be removed without seriously affecting the model，it should be removed（Coles，2001，p.109；Walker，Maddan，&Walker，2013，p.177）——has made the existence of the diamond model groundless.

Polynomial regression

In response to concerns about difference scores，Edwards and colleagues（Edwards（1994）；Edwards and Parry（1993））suggested using polynomial regression to assess differences.Instead of collapsing the component measurements into a difference score or PSI，polynomial regression includes the two variables，i.e.，the perceived effects on self and others，as well as the interaction between them and higher-order terms of the two variables，i.e.，the quadratic and cubic effects，as independent variables.Because the two components and the dependent variable，e.g.，support for censorship，are all unique，the effect of difference can be depicted in three-dimensional surface plots with response surface methodology.

The general form of polynomial regression with only the quadratic effect is（Edwards，1994；Edwards&Parry，1993）：

Constrainingβ2=-β1，β4=-2β3，andβ3=β5 in Equation（13）produces the following equation：

Nonetheless，if some more restrictive constraints，i.e.，β2=-β1，andβ3=β4=β5=0，are imposed，Equation（13）becomes the familiar simple difference score model.Consequently，Equation（13）is essentially a general case of the equation that examines both the linear and quadratic effects of difference on y（Tisak&Smith，1994），while all of the difference score models exert untested and often unfounded constraints.Models with different degrees of constraints can be compared（e.g.，the R squared change），inasmuch as they are nested in each other.The full model（Equation（13）），which uses five predictors（the perceived effect on self，the perceived effect on others，self-squared，others squared，and the product of self and others），yields a surface that can have slope，curvature and tilt and that can test virtually any functional form of difference.The detailed application of polynomial regression，as well as response surface methodology，will be given in the analysis section.

The mathematical analysis performed above，i.e.，Equations 3 through 6，have clearly demonstrated，and some scholars（e.g.，Chiou&Spreng，1996；Edwards，2001，2002；Tisak&Smith，1994）have also found，the relationships between the reliability of the difference score and the reliabilities and correlations of the two component variables，so two hypotheses were asserted.

Hypothesis 1a：the stronger the positive correlation is between the two components，i.e.，the perceived effect on self and others，the lower the reliability of the difference score is.

Hypothesis 1b：the stronger the negative correlation between the two components is，the higher the reliability of the difference score is.

Hypothesis 2：the higher the reliabilities of the two components are，the higher the reliability of the difference score is.

In addition to the hypotheses，there are some other possible factors，e.g.，variances，which have not been examined，affecting the reliability of the difference score in a more complex manner.Two research questions were，therefore，raised.

RQ1：how do the variances of the two components affect the reliability of the difference score？

RQ2：how do the reliabilities and variances of the components and the correlation between them affect the reliability of the difference score dynamically？Specifically，how will the reliability of the difference score end if the reliabilities and variances of the components are equal，and what if the correlation between the components is zero or perfect？

Application example of mathematical equations

Before addressing the hypotheses and research questions，an application example is given to illustrate how various models of addressing difference play out based on a real study of the TPE.

Four models were estimated（see Table 1）.The predictors in Model 1，a baseline model with only the two component variables as predictors，were significant，and the R squared was 0.602.Strictly speaking，Model 1 did not operationalize difference.The effect of the difference score in Model 2，the simple difference score model，was significant，but the R squared value was only 0.078.This finding invalidates the difference score model.All of the predictors in Model 3，the diamond model，were significant.The R squared value of Model 3，however，was exactly the same as that of Model 1.As reviewed above，Model 3 was more complex than Model 1.According to the parsimony principle explained above，Model 3，i.e.，the diamond model，should not be used.All of the predictors except for the intercept in Model 4，i.e.，the polynomial regression model，were not significant.The effects of perceptual difference between self and others were，in fact，inconsequential，based on polynomial regression.

This application example shows that first，the diamond model is no better than the baseline model with only two component variables；second，the simple difference score model has poor explanatory power（a very low R squared value）；and finally，none of the predictors is significant when estimated using polynomial regression.In summary，use of both the simple difference score model and the diamond model should be discouraged.

Methods

Design

The main purpose of the present paper is to determine whether the difference score is reliable and what affects the reliability of the difference score.The effects of various conditions that potentially affect reliability must be compared.A real dataset is not able to fulfill such an aim，so a computer experiment is undertaken.Because the primary issue with difference scores is their questionable reliabilities，the data were simulated based on reliabilities.As a result，the sources of low reliabilities，as well as the effects of reliabilities on TPE regression coefficients，can be empirically examined.

The author aimed to simulate three random variables，one of which is the dependent variable（e.g.，support for censorship）and the remainder of which are the two component variables representing the perceived effects on self and others，respectively.This is a simple example of the TPE scenario.As seen from Equation 4，the reliability of difference scores is related to variances in the original reliabilities of component scores and correlations between them.Based on one single covariance matrix with known means，a dataset simulating the original observations can be generated.Therefore，to generate the dataset comprised of three primary variables of interest，we designed a computer experiment，in which there are 1，000 variances（ranging from 0.5 to 100），1，000 correlations between them（ranging from-1 to 1），and three equal constant means（20）of the variables.In each simulation，1，000 observations were requested.As a result，there are 1，000 datasets and 1 million observations in total.Furthermore，based on the 1，000 datasets，the reliabilities of the difference score and sum of the two component variables and the regression coefficients（T values）of the relevant operationalizing methods（e.g.，the simple difference score and the diamond model）were estimated.Consequently，a finalized dataset with a sample size of 1，000 was generated.

The computer experiment is based on randomly generated numbers.To ensure there is no bias in the procedure of random number generation，a variety of seeds for generating pseudo-random numbers were tested，and the results of subsequent analyses were consistent.All of the above-mentioned procedures and subsequent analyses were conducted using R open source statistics software，version 3.0（Team，2015），as well as its associated packages.

Results

Factors affecting the significance of difference scores

Based on the original dataset，the outcome variable（e.g.，support for censorship）is predicted by the difference score；then，the T values of the difference score are tested as the dependent variable in the following analysis.The reliability of the difference score as the only predictor significantly affects the T value of difference scores（β=.004，p=.05；see Table 2）.The factor affecting the Understandably，the greater the reliability of the difference scores is，the more likely it is that the difference score will significantly predict the outcome variable.Consequently，the question becomes the factors that affect the reliability of difference scores，which will be addressed in detail below.

Factors affecting the reliability of difference scores

Correlations.Before formally examining the factors affecting the reliability of difference scores，a zero-order correlation matrix was generated.As seen in Table 3，there appears to be no relationships among these variables at all.An intuitive suspicion about what is causing such a result indicates the correlation between the component variables（i.e.，the perceived effects on self and others，the notation of which is correlationcomponents to avoid confusion）.The dataset is thus split into three subsets，i.e.，with positive，negative and zero correlations between the component variables.When there is literally not any correlation between the two component variables，the reliability of the difference score has a perfect correlation with that of the sum of the two component variables.In other words，they are basically the same thing.The reliability of the difference score also has a very strong correlation with the two reliabilities of the two component variables（.85 and.58，respectively；see Table 4）.

When the correlation between the two component variables is negative，there is a modest negative correlation（-.37）between the correlationcomponents and the reliability of the difference scores（see Table 5）.That is，the stronger the negative correlation between the two component variables is，the greater the reliabilities of the difference score are.Furthermore，there exists a strong positive correlation（.52 and.56）between the reliabilities of the component variables and the reliability of the difference scores.Although this finding is intuitive，such a correlation almost disappears when the correlationcomponents is positive（see Table 6）.It has a very similar pattern to that for the full data with regard to the relationships between concerning variables and the reliability of the difference score.Nevertheless，the reliability of the sum of the two components（part of the diamond model）has modest and strong positive correlations with correlationcomponents and with the reliabilities of the two component variables，respectively.The paradox of the diamond model has appeared obvious so far.The reliability of the difference score benefits from a negative correlationcomponents，yet the high reliability of the sum of two components requires a positive correlationcomponents.Apparently，the diamond model might be warranted only when there is a zero correlationcomponents，which is nevertheless a condition that is rarely met in real studies.

Correlations are informative in terms of revealing associations without regard for other confounding factors，yet finding the determinants affecting the reliability of the difference score entails regression analyses.

Regression analysis.Corresponding to the two hypotheses，the author performed a hierarchical linear regression analysis，in which the dependent variable is the reliability of the difference score and the independent variables，including the reliabilities as well as variances of the two component variables，and the correlations between the two components were tested in different blocks.Among the independent variables，we should be very cautious when interpreting the effects of correlation between the two components in that a high negative correlation value does not indicate a weak correlation but the opposite.That is，the stronger the negative correlation between the components becomes，the greater the reliability of the difference score will be.Therefore，the full dataset was split into three sub-datasets according to zero，negative and positive correlations，respectively.

Similar to the results based on the full dataset，when there is a positive correlationcomponents，there is still only a significant negative effect of correlationcomponents（β=-230.8，p<.05；see Table 7）.Nonetheless，except for the variances，all of the effects are significant when the correlationcomponents is negative（Table 8）.The correlationcomponents has a significant negative effect（β=-.219，p<.001）.That is，the stronger the correlation is between self and others，the greater the reliability of the difference score is.In addition，when the correlationcomponents is zero or negative，the reliabilities of both components have a significant positive effect（β=.36，p<.001；β=.37，p<.001）.That is，the higher the reliabilities of both components are，the higher the reliability of the difference score is.As a result，H1a，H1b and H2 are supported.

Response surface methodology.The multiple linear regression procedure is able to examine the effect of a certain predictor while controlling for other factors，but it is inferior to polynomial regression in terms of discovering complex relationships，e.g.，interaction，and higher order effects.Response surface methodology is based on polynomial regression，and it is also able to investigate various effects visually using surface plots.

Polynomial regression analyses，with the reliability of difference scores as the criterion variable and the correlationcomponents，reliabilities，as well as variances of the two components，as predictors were performed based on the full data and on the datasets with positive and negative correlationcomponents，respectively.Two predictors are equal along the dashed lines in each surface plot，while one of the predictors is greater than the other along the other diagonal line.Moreover，the predictor on the left half along the dashed line is greater than the other predictor on the right half.All the variables have been recoded on a scale anchored at-1 and 1.

Panel A in Fig 2 shows that the response has a valley（the minimum point）when the two variances are equal and have medium values.The response is greater when either of the variances or both are close to zero.Panel B in Fig 2 demonstrates that the response also has a valley when the two reliabilities are equal and have medium values.The response is greatest when both reliabilities are equal，and either is zero or close to 1.This finding is quite counter-intuitive.Clearly，the correlationcomponents plays a large role here.Panels C and D share a very similar pattern，which has the shape of a saddle.The response is greater when correlationcomponents is zero，and it becomes increasingly smaller with the increase in correlationcomponents.

The surface plots based on a positive correlationcomponents（Fig 3）are fairly similar to those based on the full data.A notable finding concerns panel C，in which a medium positive correlation results in the maximum value of the reliability of the difference score，regardless of the values of the reliabilities and variances of the component variables.If the correlationcomponents is positive，both an overly large and a trivially small correlationcomponents are detrimental to the reliability of the difference score.

Fig 4 displays the surface plots of relationships among the aforementioned variables when the correlationcomponents is negative.Panel A shows that its pattern，which is a shape close to a dome，is exactly opposite of that based on the full data.Large and equal variances are conducive to the reliability of difference scores when the correlationcomponents is negative.As shown in panel B，the reliabilities of the two components have a positive effect on the response，which is in the shape of a rhombus.It reaches the maximum point when the reliabilities are equally greatest.When the correlationcomponents is the smallest，the response has a minimum point.It has a maximum point when the correlationcomponents is greatest，and either reliability of the components is also greater.Both reliabilities have positive effects on the response（panel C）.Panel D has a similar pattern to panel C，except that the variances do not exert any influences on the response.

Concluding remarks

The significance of an outcome variable（e.g.，support for censorship）is significantly accounted for by the reliability of the difference score，which is found to be primarily affected by the correlationcomponents.Based on the full data，the correlationcomponents has a negative effect on the reliability of the difference score.This pattern persists when relying on the dataset with a positive correlationcomponents.The effects of the predictors are fairly similar when the datasets have zero and negative correlationcomponents.The stronger the negative correlation is between the two component variables，the greater the reliabilities of the difference scores are.Furthermore，the greater the reliabilities of the two components are，the greater the reliability of the difference score is.RSM extends the capabilities of the multiple regression by visually examining these above-mentioned effects.All in all，the reliability of the difference score will be better if there is no correlationcomponents or a highly negative correlationcomponents.In addition，the reliabilities of the component variables positively affect the reliability of the difference score，and the impact will be more dramatic if there is no correlationcomponents or a negative correlationcomponents.In addition to those causes revealed by the previous scholars noted in the literature review section，the diamond model has been shown to be troublesome in that the reliability of the sum of the component variables requires a high correlationcomponents.When a positive correlationcomponents is present，a modest positive correlation（as a rule of thumb，less than.5 but greater than.1）is less harmful to the reliability of the difference score.

The implications of the findings are explicit.Difference scores are not good measurements of the construct of difference.If difference scores must be used，several restrictive conditions must be satisfied.If a zero correlationcomponents is not possible，a high negative correlationcomponents is desirable.Indeed，a high positive correlationcomponents indicates only that the perceptions of self and others are so similar that no difference can be discerned at all.Moreover，the high reliabilities of the original component variables are necessary.When these conditions are met，difference scores may be used in the studies of TPE.With regard to the diamond model，Schmierbach et al.（2008）once expressed their uncertainty about“whether the diamond model...conclusively addresses the potential problem that a significant subtractive term might really reflect variance due entirely to perceived effects on self or other in isolation”.The present paper has discovered the problems associated with this model.The growing volume of studies using the diamond model has mainly resulted from a hypercorrection to the means of difference scores；the use of this model is discouraged.Difference scores are popular simply because they are intuitively appealing or computationally convenient（Peter et al.，1993）.The abuse of difference scores and the failure to adopt promising alternatives，e.g.，polynomial regression，are unfortunate because the underlying problems surrounding difference scores have been disregarded.

In summary，difference scores are incapable of measuring what they purport to measure，i.e.，the validity problem.In addition，the reliability of difference scores is compromised under various conditions.The diamond model，which is an old and rarely used method，seems to have been revived in the field of communication.It has nevertheless been demonstrated to be problematic and should not be used.Polynomial regression is the most general method because it is able to accommodate varieties of scenarios in operationalizing difference.Complemented with surface response methodology，polynomial regression is also able to present graphically the dynamic relationships between components（self and others）and the outcome variable.Therefore，polynomial regression is preferable for operationalizing the construct of difference.

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