¹ Notably: Butler, D. and Stokes, D., Political Change in Britain (London: Macmillan, 1969)Google Scholar; Särlvik, B. and Crewe, I., Decade of Dealignment (Cambridge: Cambridge University Press, 1973)Google Scholar; Heath, A., Jowell, R. and Curtice, J., How Britain Votes (Oxford: Pergamon Press, 1985)Google Scholar; and Heath, A., Jowell, R. and Curtice, J., Understanding Political Change (Oxford: Pergamon Press, 1991).Google Scholar

² Rose, R. and McAllister, I., The Loyalties of Voters (London: Sage Publications, 1990).Google Scholar

³ See Dunleavy, P., ‘The Political Implications of Sectoral Cleavages and the Growth of State Employment’, Political Studies, 28 (1980), 364–83 and 527–49.CrossRefGoogle Scholar

⁴ See Johnston, R. J., ‘A Note on Housing Tenure and Voting in Britain, 1983’, Housing Studies, 2 (1987), 112–21.CrossRefGoogle Scholar

⁵ Johnston, R. J., Pattie, C. J. and Allsopp, J. G., A Nation Dividing? (London: Longman, 1988).Google Scholar

⁶ An important third relevant spatial scale within Great Britain is country – England, Scotland and Wales. The latter two have particular political parties contesting all constituencies, along with the three that contest all, or virtually all, in Great Britain. For technical reasons, however, we are currently unable to incorporate this further scale in our multi-level modelling work, as current software can only estimate complex models (with random slopes) with no more than three levels.

⁷ An exception is Wright, G. C. Jr, ‘Contextual Models of Electoral Behavior: The Southern Wallace Vote’, American Political Science Review, 71 (1977), 497–508.CrossRefGoogle Scholar

⁸ Curtice, J. and Steed, M., ‘Electoral Choice and the Production of Government’, British Journal of Political Science, 12 (1982), 249–98.CrossRefGoogle Scholar See also Steed, M., ‘The Core-Periphery Dimension of British PolitiCs’, Political Geography Quarterly, 5 (1986), S91–S103.CrossRefGoogle Scholar

⁹ Pattie, C. J., Johnston, R. J., Fieldhouse, E. and Russell, A. T., ‘A Widening Regional Cleavage in British Voting Behaviour, 1964–1987: Preliminary Explorations’, in Crewe, I., Norris, P., Broughton, D. and Denver, D., eds, British Parties and Elections Yearbook 1991 (Brighton, Sussex: Harvester-Wheatsheaf, 1991), pp. 121–44Google Scholar; Johnston, R. J., Pattie, C. J. and Russell, A. T., ‘Dealignment, Spatial Polarisation and Economic Voting: An Exploration of Recent Trends in British Voting Behaviour,’ European Journal of Political Research, 20 (1992), forthcoming.Google Scholar

¹⁰ Johnston, , Pattie, and Allsopp, , A Nation Dividing?Google Scholar

¹¹ See Steed, , ‘The Core-Periphery Dimension’.Google Scholar

¹² Rose, and McAllister, , The Loyalties of Voters.Google Scholar

¹³ For example, Pattie, C. J. and Johnson, R. J., ‘Embellishment and Detail?’ Transactions, Institute of British Geographers, NS15 (1990), 205–26.CrossRefGoogle Scholar

¹⁴ For a fuller description, see Jones, K., ‘Specifying and Estimating Multi-Level Models for Geographical Research’, Transactions, Institute of British Geographers, NS16 (1991), 148–59CrossRefGoogle Scholar; and Jones, K., Multilevel Models for Geographical Research (Norwich: Concepts and Techniques in Modern Geography, Environmental Publications, 1991).Google Scholar

¹⁵ In the terminology of multi-level modelling, random means allowed to vary, not haphazard.

¹⁶ Throughout this article, age for each individual is measured as that person's deviation from the mean age for the entire sample.

¹⁷ See fn. 15 above.

¹⁸ This is an aspect of multi-level modelling that makes it particularly valuable for the analysis of British Election Study (BES) data. In the surveys conducted for the BES, the respondents are selected according to cluster sampling designs (as described in Butler, and Stokes, , Political Change in BritainGoogle Scholar, and Heath, et al. , How Britain Votes).Google Scholar This introduces spatial autocorrelation: people living in the same area within a constituency – in this case, a polling district, which is the sampling frame used – are more likely to be similar in their socio-economic characteristics, for example, than are people selected randomly from within the entire constituency. This introduces imprecision to the estimation of relationships at the individual level (between age and voting, for example): by explicitly including the constituencies as a higher level, multi-level modelling automatically overcomes the problems of mis-estimated precision that are inherent in a clustered, multi-stage sampling design.

¹⁹ The lines on the graph (a) in Figure 1c are drawn to extend from the minimum to the maximum age in each constituency, for it is good practice not to ‘predict’ beyond the range of the available data.

²⁰ Paterson, L. and Goldstein, H., New Statistical Methods for Analysing Social Structures: An Introduction to Multilevel Models (London: Institute of Education, forthcoming).Google Scholar Their advice stems from educational research, and it may be possible to manage with a smaller sample if the contextual effects for constituencies are greater than those for schools.

²¹ For fuller details, see Wrigley, N., ‘The Use of Percentages in Geographical Research’, Area, 5 (1973), 183–6.Google Scholar

²² McCullagh, P. and Nelder, J. A., Generalized Linear Models (London: Macmillan, 1986).Google Scholar

²³ Goldstein, H., ‘Nonlinear Multilevel Models’, Biometrika, 78 (1991), 45–52CrossRefGoogle Scholar; Longford, N., ‘Multilevel Models for Data with a Non-Normal Distribution’, Multilevel Modelling Newsletter, 2 (1990), p. 2.Google Scholar

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²⁵ Longford, N., Manual for VARCL (Princeton, NJ: Education Testing Services, 1988).Google Scholar

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³⁰ For details of the survey, see Heath, et al. , Understanding Political Change.Google Scholar

³¹ Johnston, , Pattie, and Allsopp, , A Nation Dividing?Google Scholar

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³⁴ The places are indeed the observations, and the greater the number the better. Having many voters provides information on the relationships between response and predictor variables within a place, but many places are needed to estimate the differences between places.

³⁵ Heath, et al. , How Britain Votes.Google Scholar

³⁶ Dunleavy, , ‘The Political Implications’.Google Scholar

³⁷ Johnston, R. J., Pattie, C. J. and Johnston, L. C., ‘Great Britain's Changing Electoral Geography’, Tijdschrift voor Economische en Sociale Geografie, 81 (1990), 189–206.CrossRefGoogle Scholar

³⁸ To avoid confusion, logits will be given in the text with decimal points; when transformed into proportions they are multiplied by 100 and given as percentages.

³⁹ This rule of thumb is used because the exact distribution theory is not known; the advice is to treat ‘marginal’ significance with care. See Raudenbush, S. W. and Bryk, A. S., ‘A Hierarchical Model for Studying School Effects’, Sociology of Education, 59 (1986), 1–17.CrossRefGoogle Scholar

⁴⁰ As degrees of freedom increase, Z-ratios equate to t-ratios.

⁴¹ As indicated above, the level-1 variance is set to 1.00, so the autocorrelation coefficient is 0.88/(1 + 0.88) = 0.47.

⁴² In a perfectly designed and executed survey, these forty areas would indeed be the safest seats in the country for either the Labour or Conservative parties. There are few surprises in the list, indicating a generally representative sample, the exceptions being Thurrock, Walsall North, Tynemouth, Nottingham South, Renfrew West and Inverclyde, and Blyth Valley. In the case of Renfrew West and Inverclyde, it may seem odd that this was ‘the most pro-Labour place in the sample’, when in fact the Conservative party won the seat in 1983. The similar finding in Model B indicates that the place was the most pro-Labour, given the characteristics of its population. It should also be noted that the cluster sampling procedure used in the BES may have resulted in the selection of a polling district that was very unrepresentative of the constituency as a whole. This calls for further work which uses the polling district as one of the levels in a multi-level model, an approach which is as yet not possible due to the inability to estimate complex models at more than three levels with existing software.

⁴³ The estimates are obtained by inserting the relevant data into the model. Thus, to take a complex illustration based on Model B, one estimated logit is: −0.20 [the constant term] + 0.84 [if the respondent is unemployed] + 1.30 [if the respondent is a council tenant] + (−0.02 *−26) [the differential for a 20-year-old] + 1.43 [the differential for living in Blaenau Gwent]. This sums to + 3.89 for an unemployed, 20-year-old council tenant living in Blaenau Gwent. The transformed percentage is obtained as [exp(L _ij)]/[1.0 + exp(L _ij)], which is [exp^3.89]/[1.0 + exp^3.89], which is 99 per cent.

⁴⁴ On the latter point, see also Russell, A. T., Johnston, R. J. and Pattie, C. J., ‘Thatcher's Children: Exploring the Links between Age and Political Attitudes’, Political Studies (forthcoming).Google Scholar

⁴⁵ Notably Rose, and McAllister, , The Loyalties of Voters.Google Scholar

⁴⁶ See, for example, Johnston, R. J., ‘The Geography of the Working Class and the Geography of the Labour Vote in England, 1983’, Political Geography Quarterly, 6 (1987), 7–16CrossRefGoogle Scholar; McAllister, I., ‘Social Context, Turnout and the Vote’, Political Geography Quarterly, 6 (1987), 17–30CrossRefGoogle Scholar; McAllister, I. ‘Comment on Johnston’, Political Geography Quarterly, 6 (1987), 45–50CrossRefGoogle Scholar; Johnston, R. J. and Pattie, C. J., ‘Family Background, Ascribed Characteristics, Political Attitudes and Regional Variations in Voting within England, 1983’, Political Geography Quarterly, 6 (1987), 347–9.CrossRefGoogle Scholar

⁴⁷ Dulwich has a zero logit. This does not mean that it is an extremely marginal seat but that its voters do not differ from the countrywide average pattern in their relative support for Conservative and Labour.

⁴⁸ These percentages are computed as illustrated in fn. 42.

⁴⁹ Jones, , ‘Specifying and Estimating’.Google Scholar

⁵⁰ ‘Under-dispersion’ occurs when the level-1 random term is significantly less than 1.00. There is thus less variation at the voter-level than would be expected if the conditional probability of voting Labour followed a pure binomial distribution. See Goldstein, , ‘Nonlinear Multilevel Models’.Google Scholar

⁵¹ This may also be because all of the working-class respondents in those constituencies (more exactly, the polling districts selected within them) are relatively old and younger residents are not working-class. The result may be an artefact of the data collection, however, specifically an interviewer effect. One study found that, using an ML approach, not only did some interviewers find more disability than others, but that they also elicited different relationships with age. See Wiggins, R. O., Longford, N. and O'Muircheartaigh, C., A Variance Components Approach to Interviewer Effects (London: Joint Centre for Survey Methods Research, Working Paper 2, 1990).Google Scholar

⁵² Software crashes were experienced when the class variables and the tenure categories were allowed to be random at the constituency level. This is caused by insufficient data to estimate the covariances in the random part, as this requires that each type of class or category be present in each constituency; with only around nine respondents in each seat, this was not always the case. It is possible to estimate the level-2 variances while constraining the covariances to zero, but this is not a recommended procedure when the variables that are being allowed to vary at the higher level form a dummy variable set: see Longford, , Manual for VARCL.Google Scholar One other model, in which the effects for unemployment were allowed to vary between constituencies, did successfully converge, but the associated variance did not approach significance.

⁵³ Johnston, R. J., A Question of Place (Oxford: Basil Blackwell, 1991).Google Scholar

⁵⁴ Johnston, R. J. and Pattie, C. J., ‘Class Dealignment and the Regional Polarisation of Voting Patterns in Great Britain, 1964–1987’, Political Geography, 11 (1992), 73–86CrossRefGoogle Scholar; Johnston, R. J., Pattie, C. J. and Russell, A. T., ‘Dealignment, Spatial Polarisation and Economic Voting’, European Journal of Political Research, 20 (1992)Google Scholar, forthcoming.

⁵⁵ Griffiths, M. J. and Johnston, R. J., ‘What's in a Place? An Approach to the Concept of Place as Illustrated by the British National Union of Mineworkers' Strike, 1984–85’, Antipode, 23 (1991), 185–213.CrossRefGoogle Scholar

⁵⁶ This may well indicate that there is a greater ‘bed-rock’ support for Labour in the South East than in the Industrial North East. Once individual social background, constituency milieux influences and local economic voting have been screened out we have accounted for all of the Labour voting in the Industrial North East, whereas the Outer South East still has some pro-Labour voters not accounted for by those influences. This might possibly be the outcome of embourgeoisement: see Johnston, R. J., ‘“Embourgeoisement”, the Property-Owning Democracy and Ecological Models of Voting in England’, British Journal of Political Science, 11 (1981), 499–503).CrossRefGoogle Scholar

⁵⁷ Johnston, , A Question of PlaceGoogle Scholar; Griffiths, and Johnston, , ‘What's in a Place?’Google Scholar

⁵⁸ Jones, , Multilevel Models for Geographical Research.Google Scholar

⁵⁹ Personal communication with Prof. Goldstein.

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