Salvation's Song: insights into Salvationist missiology from practices of communal singing at New Addington Salvation Army Community Church

This thesis addresses two questions: What is the lived experience of singing for members of New Addington Salvation Army Community Church? What are the implications for Salvationist missiology and practice arising from analysis of that experience? As a Salvation Army officer leading both a church congregation and a community choir, I have a particular interest in these questions as they pertain to the role of singing in mission. The research methodology is qualitative, with participants creatively exploring their relationship to singing within The Salvation Army. Participants were purposively selected, encouraging the involvement of those least likely to put themselves forward. The thesis also considers extracts from my research journal, reflections on which provide insights into the themes explored and conclusions reached. Participant data is brought into critical dialogue with the conceptual framework, which draws upon the theoretical perspectives of missiology and ethnomusicology. Notable themes emerging from the participant data are ‘belonging’, ‘emotion’, ‘spirituality’ and ‘transformation’. Reflection upon the missiological literature resulted in the proposal of five missional ‘ways of being’ which are; the facilitation and nurture of community; the empowerment for and engagement in ministry; the integration of internal structures with external action; the authentic communication of the truth; the embodiment and enactment of Christian hope. These five ‘ways of being’ are considered in light of the participant data, and singing’s contribution to these aspects of mission is demonstrated. The research demonstrates that singing provides a ‘third-space’ for the facilitation and nurture of community; its impact on wellbeing empowers singers to participate in ministry; singing generates a virtuous circle of benefits which motivate, equip and enable singers for outward actions; singing can make biblical truths accessible, encourage new selfunderstanding, and embrace non-Christians within the embodied witness to the gospel; singing’s psychological and social benefits offer present comfort and glimpses of future hope. The research concludes that the more holistic one’s view of mission, the more blurred the boundaries between the church and the world, particularly concerning participation in the missio Dei. The thesis ends by considering the implications for my own practice and the wider implications for The Salvation Army arising from the research

Supplement 1. Matlab code for testing the hypothesis of time homogeneity by parametric bootstrap.

<h2>File List</h2><blockquote> <p><b>Supplement 1, original</b> </p> <p><i><b>All files at once</b></i></p> <blockquote> <p><a href="Spencer_code.tar">Spencer_code.tar</a></p> </blockquote> <p><i><b>Matlab code</b></i></p> <blockquote> <p><a href="get_Q_like.m">get_Q_like.m</a></p> <p><a href="ML_Q_est5.m">ML_Q_est5.m</a></p> <p><a href="mlq_ufun3.m">mlq_ufun3.m</a></p> <p><a href="multinomial.m">multinomial.m</a></p> <p><a href="plike.m">plike.m</a></p> <p><a href="Qfromest.m">Qfromest.m</a></p> <p><a href="Qmatrix_bootstrap.m">Qmatrix_bootstrap.m</a></p> <p><a href="stationary_probt.m">stationary_probt.m</a></p> <p><a href="sorted_eigs.m">sorted_eigs.m</a></p> <p> </p> </blockquote> <p><i><b>Example data</b></i></p> <blockquote> <p><a href="example_data.mat">example_data.mat</a></p> <p> </p> </blockquote> <p><b>Supplement 1, Revision 1</b></p> <blockquote> <p><a href="suppl-1R1.htm">Download files</a> </p> </blockquote> </blockquote><h2>Description</h2><blockquote><p> </p> Matlab code for the bootstrap analysis in Spencer and Susko, Continuous-time Markov models for species interactions. Tested under Matlab release 14. Requires the optimization toolbox. <br> The main function, ML_Q_est5.m, tests the hypothesis that the data can be explained by a homogeneous continuous-time Markov model against the more general alternative that rates are not homogeneous. It first estimates parameters for a homogeneous continuous-time Markov model, then calculates the likelihood ratio between this model and the maximum likelihood discrete-time model. It then generates parametric bootstrap samples from the estimated homogeneous continuous-time model to generate a distribution of the likelihood ratio under the hypothesis of time homogeneity. For detailed instructions on usage, type help ML_Q_est5 in Matlab. Typical usage: <p> [Q,negl,nobs,neglobs,neglz,twodelta,p,timetaken]=ML_Q_est5(P,obs_csum,reps,nsites,ntimes);</p> <p> The inputs are:</p> <p>P is the observed transition matrix for time step of 1 unit.</p> <p>obs_csum is the number of observed transitions from each state.</p> <p>reps is number of parametric bootstrap reps to run.</p> <p>ntimes is number of time periods sampled in original data.</p> <p>nsites is number of sites sampled in original data.</p> <p> The outputs are:</p> <p>Q is the estimated homogeneous instantaneous rate matrix, with all off-diagonal elements constrained to be positive.</p> <p>negl is partial negative log likelihood for this Q matrix.</p> <p>nobs is an array of number of observations of each transition (with some rounding if the P matrix wasn't reported exactly).</p> <p>neglobs is partial negative log likelihood if we use observed transition frequencies (which are the ML estimates in a discrete-time model, not requiring homogeneity in continuous time).</p> <p>neglz is partial negative log likelihood if we set any tiny elements of Q (<2*eps, where eps is machine precision) to zero. This is usually almost identical to negl.</p> <p>twodelta is twice difference in partial log likelihoods between the Q matrix and the empirical P matrix: first row is observed, remaining reps rows are from parametric bootstrap. First col is for the Q matrix as estimated, second is with tiny elements of Q set to zero.</p> <p>p is proportion of reps with twodelta >= observed (first col Q as estimated, second col with tiny elements of Q set to zero).</p> <p>timetaken is clock time used.</p> <p>The other functions (mlq_ufun3.m, get_Q_like.m, Qmatrix_bootstrap.m, stationary_probt.m, sorted_eigs.m, Qfromest.m, plike.m, multinomial.m) are called by ML_Q_est5.m.</p> <p>example_data.mat contains the data described in the paper (Matlab format, compatible with version 6 and later). The original source for these data is Tanner, J., T. Hughes, and J. Connell. 1994. Species coexistence, keystone species, and succession: a sensitivity analysis. Ecology <b>75</b>:2204–2219 (Exposed Crest site, their Table 2, with additional information from J. Tanner, <i>personal communication</i>)</p> <p></p> </blockquote

Supplement 1, Revision 1. Matlab code for testing the hypothesis of time homogeneity by parametric bootstrap. Submitted 12 December 2005; Published 6 January 2006.

<h2>File List</h2><blockquote> <p><b>Supplement 1, original</b> </p> <p><i><b>All files at once</b></i></p> <blockquote> <p><a href="Spencer_code.tar">Spencer_code.tar</a></p> </blockquote> <p><i><b>Matlab code</b></i></p> <blockquote> <p><a href="get_Q_like.m">get_Q_like.m</a></p> <p><a href="ML_Q_est5.m">ML_Q_est5.m</a></p> <p><a href="mlq_ufun3.m">mlq_ufun3.m</a></p> <p><a href="multinomial.m">multinomial.m</a></p> <p><a href="plike.m">plike.m</a></p> <p><a href="Qfromest.m">Qfromest.m</a></p> <p><a href="Qmatrix_bootstrap.m">Qmatrix_bootstrap.m</a></p> <p><a href="stationary_probt.m">stationary_probt.m</a></p> <p><a href="sorted_eigs.m">sorted_eigs.m</a></p> <p> </p> </blockquote> <p><i><b>Example data</b></i></p> <blockquote> <p><a href="example_data.mat">example_data.mat</a></p> <p> </p> </blockquote> <p><b>Supplement 1, Revision 1</b></p> <blockquote> <p><a href="suppl-1R1.htm">Download files</a> </p> </blockquote> </blockquote><h2>Description</h2><blockquote><p> </p> Matlab code for the bootstrap analysis in Spencer and Susko, Continuous-time Markov models for species interactions. Tested under Matlab release 14. Requires the optimization toolbox. <br> The main function, ML_Q_est5.m, tests the hypothesis that the data can be explained by a homogeneous continuous-time Markov model against the more general alternative that rates are not homogeneous. It first estimates parameters for a homogeneous continuous-time Markov model, then calculates the likelihood ratio between this model and the maximum likelihood discrete-time model. It then generates parametric bootstrap samples from the estimated homogeneous continuous-time model to generate a distribution of the likelihood ratio under the hypothesis of time homogeneity. For detailed instructions on usage, type help ML_Q_est5 in Matlab. Typical usage: <p> [Q,negl,nobs,neglobs,neglz,twodelta,p,timetaken]=ML_Q_est5(P,obs_csum,reps,nsites,ntimes);</p> <p> The inputs are:</p> <p>P is the observed transition matrix for time step of 1 unit.</p> <p>obs_csum is the number of observed transitions from each state.</p> <p>reps is number of parametric bootstrap reps to run.</p> <p>ntimes is number of time periods sampled in original data.</p> <p>nsites is number of sites sampled in original data.</p> <p> The outputs are:</p> <p>Q is the estimated homogeneous instantaneous rate matrix, with all off-diagonal elements constrained to be positive.</p> <p>negl is partial negative log likelihood for this Q matrix.</p> <p>nobs is an array of number of observations of each transition (with some rounding if the P matrix wasn't reported exactly).</p> <p>neglobs is partial negative log likelihood if we use observed transition frequencies (which are the ML estimates in a discrete-time model, not requiring homogeneity in continuous time).</p> <p>neglz is partial negative log likelihood if we set any tiny elements of Q (<2*eps, where eps is machine precision) to zero. This is usually almost identical to negl.</p> <p>twodelta is twice difference in partial log likelihoods between the Q matrix and the empirical P matrix: first row is observed, remaining reps rows are from parametric bootstrap. First col is for the Q matrix as estimated, second is with tiny elements of Q set to zero.</p> <p>p is proportion of reps with twodelta >= observed (first col Q as estimated, second col with tiny elements of Q set to zero).</p> <p>timetaken is clock time used.</p> <p>The other functions (mlq_ufun3.m, get_Q_like.m, Qmatrix_bootstrap.m, stationary_probt.m, sorted_eigs.m, Qfromest.m, plike.m, multinomial.m) are called by ML_Q_est5.m.</p> <p>example_data.mat contains the data described in the paper (Matlab format, compatible with version 6 and later). The original source for these data is Tanner, J., T. Hughes, and J. Connell. 1994. Species coexistence, keystone species, and succession: a sensitivity analysis. Ecology <b>75</b>:2204–2219 (Exposed Crest site, their Table 2, with additional information from J. Tanner, <i>personal communication</i>)</p> <p></p> </blockquote

Appendix A. Model derivation, statistical methods, and additional results.

Model derivation, statistical methods, and additional results

Supplement 1. Matlab and C code for fitting linear and Lotka-Volterra models to transition probability data.

<h2>File List</h2><blockquote> <p><a href="linearmodels.zip">linearmodels.zip</a></p> <p><a href="LVmodels.zip">LVmodels.zip</a></p> </blockquote><h2>Description</h2><blockquote> <p>linearmodels.zip is a zip archive of Matlab code for fitting continuous-time linear Markov models to data on transition probabilities. See README.txt in the zip archive for full details.</p> <p>LVmodels.zip is a zip archive of C code for fitting Lotka-Volterra models to data on transition probabilities. See README.txt in the zip archive for full details.</p> </blockquote

Full Archive

Full Archiv

Predicted changes in log barnacle abundance (25 cm⁻²) in relation to shore height and direction.

<p>Sampling positions faced four different directions: north, south, sea, shore. Values are based on those predicted from a generalized linear mixed model output using the median value of Location (first principal component of latitude and longitude), the mean level of Rugosity of the sampling positions and exposed or sheltered levels of Exposure.</p

Examples of the life-size cast-iron statues at Crosby Beach, Liverpool.

<p>Images show two of the 100 statues that form the art installation ‘Another Place’; one at the higher end of shore height sampled (left) and one at a lower shore height (right). The statues stretch over approximately 3 km of the foreshore and are distributed at a range of tidal heights.</p

Predicted mean abundances of barnacles (25 cm⁻²) per statue position

<p><b>in relation to their location.</b> Predicted mean abundances are based on predicted values from a generalized linear mixed model output, with contours indicating actual shore height of the statues.</p

Goodness of final model fit

<p><b>used to assess barnacle abundance on the statues at Crosby.</b> Goodness of fit of the final generalized linear mixed model is illustrated through assessment of the fitted values of the selected final model against the residuals of the model (red line indicates loess smoother).</p