Quality of Life: A Longitudinal Analysis of Correlates of Morale in Old Age

This paper examines recurrent continuous morale in old age within a statistical modelling paradigm. The Anglicised Philadelphia Geriatric Centre Morale Scale was used as a small component of a major longitudinal study of old age in rural North Wales, U.K. The literature review and cross-sectional analysis of morale in old age is published elsewhere. This paper deals with the aspect of the longitudinal analysis of morale in old age. The proposed statistical modelling relates recurrent morale to a set of explanatory variables that includes subjective as well as objective measures. In order to assess the degree to which explanatory variables influence morale, an adequate statistical model must handle the possibility that substantial variation between respondents will be due to unmeasured and potentially unmeasurable variables (residual heterogeneity), multicollinearity, and past behaviour effect. These applications are illustrated using morale in old age from the North Wales Longitudinal Study Old Age. The results suggested a strong presence of heterogeneity effect, i.e., current levels of morale appear to be individual specific and independent of its previous levels.


INTRODUCTION
It is suggested that given increasing focus on chronic disease by geriatric medicine, attention to morale is an important strategy for maximizing quality of life [1]. Sullivan [1] further suggested that improvement in the care of the elderly may be possible by getting physicians to detect and treat problems in morale in old age. The literature reports a number of variables as correlates of morale in old age such as health, income, community activities, mobility, and level of social support [2]. The relationship between morale in old age, depression, and dementia is also well documented [3,4,5,6]. In practice, depression in old age is common, underdiagnosed, and undertreated [7,8,9,10,11] and poor prognosis is associated with coexisting dementia and ill health [6]. Depression in turn is related to reported health complaints [12], pain [13], and income [14]. Thus, there may be a true underlying relationship between morale and variables reported in

METHODS
The data come from a survey of elderly people living in rural North Wales [21]. The data structure is shown in Table 1A. As can be seen, three time data were available only for the old elderly (respondent who were 75+ in 1979). Furthermore, a variable of interest (the Pfeiffer dependency scores) was included in the questionnaire in 1983 and 1987 interval points. These scores are interviewers' observed health and dependency using five scales (see Appendix I), which may be seen as more objective than self-assessed state of health and other self-reported dependencies. Therefore, it was decided to restrict the analysis to the 1983 and 1987 time points. This strategy also allows the flexibility to test the past behaviour effect using data from 1979.   1  3  1  3  1  1  1  3  1  3  1  1  1  1  3  1  1   3  1  3  1  3  3  3  1  3  1  3  3  3  3  1  3  3   2  2  2  2  2  2  2  2  2  2  2  2  2  2  2 2 2

Morale Scale
The Philadelphia Geriatric Centre Morale Scale [26] was Anglicised and adapted (see Table 1B) as part of a major study of old age in rural North Wales [21,27]. This scale was used for a number of reasons: (1) it has been widely used and therefore maximises replication, (2) it has been shown to have a high correlation with the judgment of clinical psychologists [28], (3) it has been shown to be reliable with very old respondents and with rural populations, and (4) it was the only available scale at the time the study began which includes social relationships among its items [27]. Lawton [28] reported a satisfactory reliability and high internal consistency. On the basis of piloting and in order to extend the range of possible response, which Lawton felt to be desirable ( [28], p. 160), "don't know" was added to the yes/no option. A need was also felt for an aggregate measure of morale, which Lawton identified as sufficient for many research purposes ( [28], p.164). High morale item responses were therefore scored as 3 and low morale responses as 1. Those whose morale was insufficiently high or low to give an unequivocal response scored 2 as an intermediate measure as shown in the table. Aggregate morale was then calculated as an average of the 17 responses. This aggregate measure formed continuum from 1.0 (low morale) to 3.0 (high morale). There were 38 cases with a valid morale score at each interval point 1983 and 1987 in the North Wales Elderly Data. The sample size appear small, however Table 1C suggests that it is sufficiently large to detect a small difference of 0.1 on the morale scale with 5 and 20% probability of type I and type II error (power of 80%), respectively [29]. Because of the relatively small sample size, large categorical variables were collapsed into two or three categorical variables. The list of explanatory variables is shown in Appendix I.

Models for Analysis
A regression type model was specified with morale as the response variable. The advantages of a regression model over other methods, such as analysis of variance or end-point, are the ability to handle heterogeneity as well as a large number of continuous and categorical explanatory variables, to provide an estimate of the difference in the pattern of response given an explanatory variable, and to allow the estimate of not only the main effect of explanatory variables, but also first and higher order interactions between them.
For the longitudinal analysis of morale, the 1983 and 1987 data points were used, thus forming a sequence of observations on the same individuals. Fitting the conventional regression model to such data led to a well-known specification error. The regression model was modified with a "variance component" specification in which the heterogeneity effect is implicitly defined in the equation as a time constant term {θ} separately from the regression error term {ε} [30] (see Appendix II). There are two methods of model estimation for models with two unobserved components: the conditional likelihood method and the marginal likelihood method. The conditional likelihood method, sometimes referred to as the difference method, eliminates θ by subtracting the response equation for time 2 from that of time 1. This differencing leads to the term θ and all other constant variables (such as sex) to be eliminated from the model, thus restricting inference to time varying variables. The resulting model could then be fitted using the likelihood or least squares method [31,32,33]. A drawback of this method is the loss of information. However, the method is easy to adopt and apply in particular when dealing with continuous response variable measured at two time points. Furthermore, loss of information can be compensated for by integrating the instrumental variables method in the statistical modelling [34].
In this paper, the marginal likelihood method was used. This method, also referred to as the integrated likelihood method, eliminates θ by integrating it out of the likelihood equation [30,35]. This method allows time varying and time constant variables in the analysis. Notice that the independence assumption, that the error terms are independent of the included explanatory variables, must still hold. This method provides a useful statistic for the heterogeneity effect that is given by the within-individual correlation (R 2 )(see Appendix II).
The forward substitution approach was employed to model building because of the large number of explanatory variables. The computer program VARCL [36], which handles variance component models with a continuous response variable, was used for model fitting. Variables were tested in the model one at a time using the likelihood ratio (χ 2 ) and the F-ratio goodness of fit test, for the longitudinal and the pooled cross-sectional methods, respectively. The variable with the largest χ 2 and associated smallest pvalue was entered into the model next. The process was repeated with those variables, which were significant at 10% level, until there were no statistically significant variables remaining.
For comparison purposes, a cross-sectional analysis of the same data was also carried out. The standard regression model without structural modification was fitted to the data. Thus, the cross-sectional model assumes that the observations on the same individuals in 1983 are independent of the 1987, i.e., giving a total sample of (2 × 38) 76 cases.
Some authors have suggested that subjective variables may play an intervening role between objective variables and morale [2]. Variables were classified as subjective if they were subject to the respondent's interpretation [21], see Appendix I. Through their possible relationship with the omitted variables, the subjective variables are responsible for model mis-specification and erroneous results. As described in the methods section above, the longitudinal modelling approach allows control for the omitted variables.

RESULTS AND DISCUSSION
Past behaviour effect was tested within the modelling framework using dummy variables representing morale in 1979 and 1983 in the longitudinal analyses. For this data set, past levels of morale do not appear to be correlated with the present levels of morale. The results from the different methods are summarised in Table 2.
The cross-sectional method suffers from a lack of clarity due to a marginal choice between the variables "confidant" (p = 0.003) and "Pfeiffer mental rating" (p = 0.02) (one is a more limited and subjective manifestation of the other), "confidant" is selected to be included in the final model. The fitting process for the longitudinal model clearly reveals that including the cumulative rating in the model removes the high significance of both physical and mental rating, i.e., cumulative Pfeiffer dependency appears to control for the effect of both physical and mental ratings.
The results from the cross-sectional method suggest that dependency due to physical health (as measured by the Pfeiffer Scale) may lead to lower levels of morale; on average, those highly dependent individuals as shown by the physical dependency scale score lower on the morale scale. Perception of having a "confidant" appears to be positively correlated with morale; availability of "confidant" increases levels of morale as opposed to not having a "confidant" at all. It is plausible that perceived companionship in old age as reflected by "confidant" operates in the opposite direction of the effects from any lack of quality of life associated with lowered mental competence that may be affecting morale.  The results from the marginal likelihood method, allowing control for heterogeneity effect, seem to suggest no direct link between subjective variables and morale for this data set. The objective variable "cumulative Pfeiffer" dependency measure appears to control for the effect of all the other variables. The high within-individual correlation (R 2 = 0.66, Table 3) emphasizes the importance of adopting a methodology that allows control for heterogeneity effect. The results from this model suggest that those with higher physical health dependency, as measured by the cumulative Pfeiffer score, on average, score 0.25 (5*-0.05) lower on the morale scale (other characteristics being the same). The within-individual correlation of (R 2 = 0.66) confirms the substantial heterogeneity effect in the data which means that temporal dependencies of morale in old age is due to heterogeneity rather than previous state of morale, i.e., those who currently appear to be of low morale are inherently so. This result highlights the important role of panel data and methodologies that allow control for this effect.

CONCLUSION
It is reassuring to note that, given the size of the sample, the results appear robust, which is indicated by the small parameter estimates and their standard errors. Furthermore, the model fitting approach of excluding and including subjective variables ensured the identification of the weaker effects in the data, as well as providing an idea about the role of subjective variables that is confirmed by the longitudinal modelling. On the whole, there were fewer variables to focus on than reported in the literature.
Clearly, it is important to employ panel data and methodologies that handle the heterogeneity effect. On the other hand, ignoring heterogeneity effect in the analysis may lead to spurious relationships and an overestimation of the effect of included explanatory variables. For example, while age and state of health may appear to be significantly related to morale in old age, such relationships may well be due to a correlation between age, health with depression, and frailty, which are omitted from the study. This result has implications for social and health policy development and policy evaluation. In an era where there is a heavy emphasis on evidence-based practice, this approach has clear implications for health and social policy development and evaluation. In this context, evidence must be based on relevant and appropriate information.

APPENDIX II: INTEGRATED OR MARGINAL LIKELIHOOD METHOD
Consider the conventional regression model: where x is the vector of explanatory variables, β is the vector of the regression parameters, and ε is the vector of i.i.d regression error. Longitudinal data structure form a hierarchy of clusters, i.e., individual i at time t 1 , t 2 ,..., T N form cluster i which will be more similar than those in other clusters. When applying the conventional regression model, the equation above violates the independence assumption; explanatory variables x may be correlated with the i.i.d error ε due to observations on the same individual in each cluster. To some extent, this problem can be overcome by adopting a "variance component" specification, including an individual specific error term into the equation [30] as follows: where θ is the vector of additional individual specific error or residual heterogeneity. The error terms are assumed i.i.d and to be independent of the x. Notice that the nuisance parameter θ is time constant. With the longitudinal approach, past behaviour could easily be introduced as the sequence of response observed at the previous time point y it-1 as follows: for time t y it = {αy it-1 } + βx it + θ i + ε it for time t+1 y it+1 = {αy it } + βx it+1 + θ i + ε it+1 To operationalize this model, we must eliminate θ before model fitting because it is not possible to estimate the nuisance parameter simultaneously with the structural parameters (see [30,35,40]).
The marginal likelihood method eliminates θ by integrating it out of the likelihood. The likelihood is based on the probability or density unconditional on θ, given by: f(S i |φ;x i ) = ∫ f(S i |β;x i ;θ) f(θ) dθ where S is the observed sequence of outcome and f(θ) is the p.d.f of θ, and the parameter vector φ consists of β and parameters of f(θ). Therefore each case contributes to the likelihood: For a sample of N individuals (with up to T times observations), the integrated or marginal loglikelihood is thus given by:

∑ ∑
The integration will lead to elimination of nuisance term θ from the model [35]. The individual specific term θ i and the i.i.d error term ε it (between intervals) are assumed to be normally distributed with zero mean, unknown variances σ 2 θ and σ 2 ε , respectively, and zero covariances. It can be deduced that the intra-individual correlation is given by [30]: For model selection and model fitting VARCL [36] was used.